Kleene Stars in Shuffle Algebras
Formal Metadata
Title 
Kleene Stars in Shuffle Algebras

Subtitle 
A (tangled) tale of various (bi)algebras

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License 
CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
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Release Date 
2021

Language 
English

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Subject Area  
Abstract 
We present some bialgebras and their monoid of characters. We entend, to the case of some rings, the wellknown theorem (in the case when the scalars form a field) about linear independence of characters. Examples of algebraic independence of subfamilies and identites derived from their groups (or monoids) of characters are *provided. In this framework, we detail the study of oneparameter groups of characters.

00:00
Commutative property
Complex (psychology)
Group action
State of matter
Multiplication sign
Mathematical singularity
Sheaf (mathematics)
LagrangeMethode
6 (number)
Explosion
Casting (performing arts)
Plane (geometry)
Different (Kate Ryan album)
Series (mathematics)
Bounded variation
Hill differential equation
Local ring
Algebra
Factorization
Proof theory
Logarithm
Fisher's exact test
Polynomial
Renormalization
Mass flow rate
Parameter (computer programming)
Variable (mathematics)
Proof theory
Tower
Time evolution
Series (mathematics)
Order (biology)
Mathematical singularity
Nichtlineares Gleichungssystem
Identical particles
Bounded variation
Physical system
Resultant
Thomas Bayes
Combinatorics
Classical physics
Neighbourhood (graph theory)
Functional (mathematics)
Real number
Algebraic structure
Routing
Algebraic independence
Linear independence
Formal power series
Thermodynamisches System
Operator (mathematics)
Modulform
Energy level
Theorem
Lie group
Nichtlineares Gleichungssystem
Antiderivative
Linear map
Multiplication
Forcing (mathematics)
Polygon
Commutator
Algebraic structure
Volume (thermodynamics)
Mortality rate
Group action
Perspective (visual)
Hausdorff space
Film editing
Algebra
Morphismus
Scalar field
Function (mathematics)
Spherical cap
Physics
Set theory
Object (grammar)
Musical ensemble
Linear independence
Superposition principle
Extension (kinesiology)
09:26
Commutative property
Group action
Latin square
Price index
Water vapor
Dimensional analysis
LagrangeMethode
Connected space
Vector space
Factorization
Structural load
Propositional formula
Infinity
Product (business)
10 (number)
Category of being
Hadamard matrix
Ring (mathematics)
Series (mathematics)
Order (biology)
Helmholtz decomposition
Mathematical singularity
Arrow of time
Summierbarkeit
Functional (mathematics)
Recursion
Directed graph
Spacetime
Beat (acoustics)
Student's ttest
Event horizon
Product (business)
Finite element method
Term (mathematics)
Boundary value problem
Modulform
Divisor
Lie group
Associative property
Maß <Mathematik>
Alpha (investment)
Compact space
Standard deviation
Physical law
Commutator
Basis <Mathematik>
Line (geometry)
Power (physics)
Function (mathematics)
Network topology
Spherical cap
Set theory
Linear independence
Family
Convolution
Beta function
Multiplication sign
Mathematical singularity
1 (number)
Sheaf (mathematics)
Uniform convergence
Icosahedron
Mereology
Grothendieck topology
Spherical cap
Physicist
Series (mathematics)
Körper <Algebra>
Category of being
Algebra
Position operator
Area
Logical constant
Polynomial
Renormalization
Mass flow rate
Associative algebra
Special unitary group
Price index
Term (mathematics)
Time domain
19 (number)
Substitute good
Proof theory
Wellformed formula
Convex hull
Right angle
Resultant
Pole (complex analysis)
Combinatorics
Polynomial
Neighbourhood (graph theory)
Statistics
Functional (mathematics)
Cliquewidth
Divisor
Observational study
Blind spot (vehicle)
Algebraic structure
Theory
2 (number)
Power (physics)
Time domain
Algebraische Kombinatorik
Linear independence
Formal power series
Network topology
IRIST
Wellformed formula
Operator (mathematics)
Electric field
Hydraulic jump
Linear map
Condition number
Shift operator
Expression
Division (mathematics)
Evolute
Numerical analysis
Plane (geometry)
Algebra
Scalar field
Morphismus
Lie group
Factory (trading post)
Object (grammar)
Diagram
Körper <Algebra>
Extension (kinesiology)
28:19
Logical constant
Commutative property
Convolution
Standard deviation
Group action
Injektivität
State of matter
Confidence interval
Multiplication sign
Water vapor
Prime number
Independence (probability theory)
Abelsche Gruppe
Duality (mathematics)
Roundness (object)
Algebraic closure
Diagram
Monster group
Algebra
Multiplication
Physical system
Polynomial
Logical constant
Associative algebra
Propositional formula
Inverse element
Term (mathematics)
Surface of revolution
Element (mathematics)
Product (business)
Fraction (mathematics)
Ring (mathematics)
Tower
Series (mathematics)
Order (biology)
Theorem
Identical particles
Bounded variation
Associative property
Polynomial
Statistics
Module (mathematics)
Link (knot theory)
Diagonal
Drop (liquid)
Surgery
Product (business)
2 (number)
Power (physics)
Time domain
Causality
Root
Term (mathematics)
Wellformed formula
Energy level
Modulform
Associative property
Maß <Mathematik>
Curve fitting
Hydraulic jump
Linear map
Alpha (investment)
Condition number
Time zone
Standard deviation
Multiplication
INTEGRAL
Quantum state
Polygon
Horizon
Exponential function
Line (geometry)
Group action
Monoid
Existence
Plane (geometry)
Positional notation
Hausdorff space
Voting
Algebra
Basis <Mathematik>
Morphismus
Combinatory logic
Spherical cap
Universe (mathematics)
Vertical direction
Partial derivative
Faktorenanalyse
Diagonal
Game theory
Coefficient
Linear independence
Limit of a function
38:19
Commutative property
Group action
Weight
Water vapor
Independence (probability theory)
Plane (geometry)
Isomorphieklasse
Algebraic closure
Category of being
Factorization
Proof theory
Potenz <Mathematik>
Logical constant
Polynomial
Observational study
Differential (mechanical device)
Correspondence (mathematics)
Propositional formula
Parameter (computer programming)
Staff (military)
Perturbation theory
Term (mathematics)
Product (business)
Derivation (linguistics)
Category of being
Fraction (mathematics)
Wellformed formula
Series (mathematics)
Time evolution
Chain
Configuration space
Nichtlineares Gleichungssystem
Identical particles
Pole (complex analysis)
Associative property
Combinatorics
Link (knot theory)
Parametrische Erregung
Algebraic structure
Element (mathematics)
Product (business)
Power (physics)
Wellformed formula
Antiderivative
Hydraulic jump
Linear map
Rule of inference
Addition
Time zone
Standard deviation
Slide rule
Projective plane
Exponential function
Group action
Limit (category theory)
Perspective (visual)
Plane (geometry)
Hausdorff space
Positional notation
Algebra
Function (mathematics)
Spherical cap
Partial derivative
Set theory
Musical ensemble
Linear independence
42:20
Commutative property
Group action
Presentation of a group
State of matter
Multiplication sign
Direction (geometry)
Sheaf (mathematics)
1 (number)
Plane (geometry)
Matrix (mathematics)
Series (mathematics)
Category of being
Algebra
Factorization
Physical system
Observational study
Propositional formula
Physicalism
Parameter (computer programming)
Product (business)
Commutative algebra
Tensor
Category of being
Time evolution
Duality (mathematics)
Nichtlineares Gleichungssystem
Identical particles
Associative property
Combinatorics
Divisor
Observational study
Diagonal
Product (business)
Element (mathematics)
Morphismus
Causality
Wellformed formula
Operator (mathematics)
Modulform
Associative property
Hydraulic jump
Linear map
Condition number
Slide rule
Projective plane
Expression
Commutator
Group action
Perspective (visual)
Plane (geometry)
Formal power series
Positional notation
Film editing
Algebra
Factory (trading post)
Spherical cap
Hydraulic motor
Linear independence
Local ring
49:12
Shooting method
Algebra
Time evolution
Spherical cap
Physics
Nichtlineares Gleichungssystem
Musical ensemble
Combinatorics
00:01
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will be no 1 10th not glop cochet vol ou this very nice how to compare to the firefighters of fiesch a folio such a cure the world's first world you take you small vertical and the second must from a small horizon which dirties the from left to right and you know from 10 10 the stations water born to this post is afraid corner you know passeuse weasel east north passes in diagonal past and bear twitts pass you can eva told him 'I didn't go to zoteux for example y reliable diagonal term ? will take five of the do letters annie fault horizontal admission pasri ipod ipod of the state they remain two horizontal world suf iam dare not from offer north step to will put the letter of poverty kloppers on now as it and this is another example ipad is will use forts and or m ay pastis suitcases empowered yesterday so we have considered faiza fun and we can say that her pays with his schaefer fault providing fabi associative reader associative algebra and we want to prove that is you to the river sean ischios ndao qishan chedrawi soap operas tools of 10 tidiane concatenation cleaner and elections an epsilon witch tale the monster of every polydor him with biaggi bras in fact hard both facs of athis delta one he points a hangglider hotel delta place in new the repeat vice of procedure of other facs of a Thai system nil potter than this algebra in fact europe en cause you can't you been there so fidji identity because you can powder identity and kohl's epsilon place high places en place in new hope you die in furs crisis we play surgery no you want to go to those who you are so if you want to go to jesus and you desplanques atention will stay from place to photos that prohibition and your eyes schaefer will take the price of delta fayoum technical conditions on dit sanchez constant 'in order to want this will not develop the style watch the bowl of sight what is it and resting iti what is in terris sting him this morning he was with fight crazes art star character except the play with the wind that you take pure state inaction line alpha ba jean philippe this link been seen it is just linear form to ben I had a lot of stars at the military nict of play and 2e azzoun au it is true said algebra of character of dedit to djibril make up louise respect and everything from god to water to delta lights on you composer on play with le fit shuttle and see the what is not so easy to prove combinator you bind to half word pi2 pedestrian way morning if you take e de level frame of the university data of fire cards love to characters in the game character jazz stadium everything is smooth formula and letters and you can prove to 10 follows golden cursor means that her it was to little this
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azura woerth bed of first height of seconds term and deal disturbances year of confession and identity eight years or to analyze groupe aoste of books at refusal of apple for example the csars not so this is now to see but a rice mill those of origin berg hancock mine and means that this is property and for every bayane gibrat bat in you know in they want the arms of two maids rid of paint in iz beau ian by and the bayou ? polygone of character soul to exist in the rye start the be on the bright and then we will make the standard decrease in fine by action to 3 those who would have missed 3itech guy says antoine halff filtration witches increase in with no suffrages it is gross filtration is compatible with the revolution product a de con que je dire cet irf this it can be done for whatever the ring of coefficient to beat non tu a all year round gobeil strong guests galgo mind is up of character is liina lind and panels with respects any risk of pollution has had an example let her live with jeanpaul witty there is all in in winter a polynomial what guides me is good from at arms of diane jay bryson girl diane diagram of polynomial czech only one varied ball delta is the delta aux ex et extenso one love takes pin's the actress gives primitive an epsilon he attacks of consent polynomial and other jumps to this our star anthem on full showcase start of the line because you have all in one time venture those of character aof two stories are useful easily beaten Czechs at 10:10 a.m. peculiarity of formula 1 to 2 of bono ide and deposit son joe biden beau for particularity this group at it is the case for every you looking at the brave at 10.6 to annals and aspivenin trigger the example at the place called the rachy all in order to have the roots the update for the memory extinction 9 blu ray the roots and you take all de prague d'un buzz a new day resorts of the prime numbers in this is from character of love keyyo ex identify as drummer in what i the pressing stadi thing to tell you it's tough characterisa jay bryson depanneur over de pauline au vote and you can first child is considering that it is a star is silver on fouad meine is zone i hope august at bmx this time with her with respect to the complete edition pro 2 add to view this in stat of inch apple power and kings tower multiplier you can't be checked synthetize alger by hippolyte debate gives confidence and furious men is variable either before entering via the network so what we consider now is the group of character and drop of character on a feat of a thing adlane la gare is it is very very easy lauga who correspond no elsewhere yes the live in to be with you i found 10
38:29
example the staff need the project took stock of the razor birds
38:39
explained laughs you the addition of in dc as perturbations sur you have the beginning the same as those annual craze why idex ipod touch this town no if you take two the zone apply it string will see formula has he general pierre fons taffel must 10:10 late staffel dstar equals this nazist icloud to pout all is one indyk chain al fault plus cattle to 10 is by linea product and cheese water fault it also makes 10 formula you can see me mathilde if you take a never limits on why why why to this project hours teens power light in a world style so you code this link robin action by jiss serristes 1007 united senio poutine a zo power you get this following women eleven you get the fallen from formula 1 red bull pole bankruptoubaz why this polling eynden johan firewall s chapple staffel saurai fayon brown of tea all apple sorry from stars took six hours and cool fayoma wife and the what plastie by the swan sodji ce will result in the fact that this is the one by bulls and has it is the one configurable week and identity which can first check back in town g?rard forme de la like for example this is the dark the planes switches character and character that are unique to the nemtsov primitive element jump 10 exploit people yves at yes we have character will be used exponential of what it is in the same as it is so they taking having had to waco ding we can use this and take you and letters for example to the standards ? la hesbaye tea and said that this is not the one per capita group it is the one permetter paf drode 22 October bat it can be lobo watkin one can take 2 log au petit paramotor care make a formula 1 opinion [Music] so is formula a candidate ball czech by other things may be so 7me plot of stars of the planes property which is not dit ficoba titrisent world to be
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minister in 10th then in baillargues and brad richards at fuse combinat th?riault neither trained nor operation offered formal power series coding hoding different sing star of the planes property in that character for this is exactly handisport so this form you learn easy as protection of groups of character
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and for pong characters yoka sheet matrix or non commutative insults is not un portable and cozy free and the bright bright dawn commutative paulino gueule non hypios consider this composition 9.6 characters him to 20 impressive pollutions or it is the rolling stones the project revolutionize pression in physics led by carole benson know if you have character which is this time y value divine statuerait is the key commutative algebra associative view against nothing contrary and wyse to customs of might have commutative well it is not himpens ozap because he has this is commutative zen e10 ymagis commutative bat wil also destroyed or if you fifi die for difforme 10 it is not necessary commutative chaud le mas stes start with his anne giscard actors identity you give me your world as we give you got words the c word 6 identity and of course i traces de charles prow portier because you this the chapel morphism his name we have here is made from diagonal series city we are the renters of the moe ue tensor dabo you and you see that it is as expression nova identity on you catch and letters from dabo yohan cabaye or everything to buy the thing duality tour octogonale bezouce orthogonale between them says it can be prophesied mayor factories exion times beland sound back above overwhelm that is easy the product of the stone age of course non ifrs of character you can't keep the identity direct from a titi showcase diagonal series which is pharma nadia and then you obtain system of local coordinate high tech data dira motors group oasis heart of groups sonata yf equippique belge are there to link algebra to the fridge you take who operates thing yoav system of local cordina hitch backpacker the unity non un computer so you see that this will give you system of local cardinet of as you know your golden house at the lease of composites is true that actor at the product of elemental character and two hands with durable des formes version 9 10 factory section and of course and is rather state for war ten faults historize associative son paste with 2 commutative cut in our assets it is generally the ball with the witch general study conditions highlight the wall thouvenot commutative disturbed everything explodes lookalikes factorization which is easy to all is in any case sometimes state is the key except researcher the in fact owls of all for all developing and the brass which are free have had a radio ski jump causes do not intervene quickly formula as you grow derived formula 1 could very quickly by this and under certain conditions production techniques you can have said orthogonal belgium which is in them say be stars when you go gebra saut channel 6:04 am dip this idea is true of the opera sowind evokes of christina bauer section swiss them the hired eve note ric ur du use this to factory are characters honor to rhode other hand volley ping at the base like the heist nistelrooy shicoff pardonne me for dit pronunciation binding the arms otherwise otherwise want to evoke in nador lee algebra which path commutative un coming from maxi saut njawe c2a yav finished with my presentation of invoices or for over you atention with big bear lake in heat described marc sur cobain it will be 25
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did not forget 5.5 sport had missed the public shoot [Music]