Extensions of usual and deform vertex algebras
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Title 
Extensions of usual and deform vertex algebras

Title of Series  
Number of Parts 
12

Author 

Contributors 

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. 
Identifiers 

Publisher 
Institut des Hautes Études Scientifiques (IHÉS)

Release Date 
2013

Language 
English

Content Metadata
Subject Area  
Abstract 
There are two natural ways to constract the new vertex algebras.One as subalgebra in the known one.Bosonisation is the special case of this construction.The second idea is opposite to get the new algebras as exstensions ,in this case we add to vertex algebra some combination of vertex operators.We discuss several examples .Some of them are related with AGT bisiness.

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State of matter
Multiplication sign
Physicalism
Mereology
Number
Mathematics
Field extension
Algebra
Computer animation
Lecture/Conference
Order (biology)
Reduction of order
Noise
Quantum
Vertex (graph theory)
Mathematician
Uniform space
Directed graph
03:15
Ocean current
Standard deviation
Product (category theory)
Element (mathematics)
Limit (category theory)
Variable (mathematics)
Mereology
Field extension
Maxima and minima
Centralizer and normalizer
Manysorted logic
Doubling the cube
Lattice (order)
Lecture/Conference
Combinatory logic
Duality (mathematics)
Conformal field theory
Reduction of order
Energy level
Right angle
Subtraction
Family
Resultant
08:02
Linear algebra
Quantum group
Multiplication sign
Laurent polynomial
Parameter (computer programming)
Student's ttest
Differential operator
Manysorted logic
Lecture/Conference
Operator (mathematics)
Quantification
Reduction of order
Energy level
Subtraction
Condensation
Addition
Numerical digit
Multiplication
Process (computing)
Theory of relativity
Spacetime
Product (category theory)
Commutative property
Generating set of a group
Infinity
Limit (category theory)
Complex number
Bilinear form
Order (biology)
Quantum
Game theory
Object (grammar)
Coefficient
Family
Directed graph
Separation axiom
17:32
Metre
Quantum group
Correspondence (mathematics)
Sheaf (mathematics)
Resonance
Parameter (computer programming)
Mereology
Dimensional analysis
Grothendieck topology
Explosion
Frequency
Centralizer and normalizer
Root
Manysorted logic
Lecture/Conference
Term (mathematics)
Queue (abstract data type)
Energy level
Field (mathematics)
Perimeter
Position operator
Condition number
Area
Series (mathematics)
Standard deviation
Independence (probability theory)
Algebraic structure
Infinity
Line (geometry)
Bilinear form
Functional (mathematics)
Local Group
Field extension
Summation
Doubling the cube
Combinatory logic
Universe (mathematics)
Order (biology)
Conformal field theory
Quantum
Right angle
Object (grammar)
Coefficient
Conformal map
Resultant
28:06
State of matter
Correspondence (mathematics)
Decision theory
Multiplication sign
Similarity (geometry)
Mereology
Rule of inference
Power (physics)
Expected value
Frequency
Group representation
Mathematics
Causality
Manysorted logic
Lecture/Conference
Term (mathematics)
Quantification
Canonical commutation relation
Field (mathematics)
Subtraction
Condensation
Condition number
Theory of relativity
Product (category theory)
Generating set of a group
Physical law
Functional (mathematics)
Local Group
Calculation
Field extension
Arithmetic mean
Commutator
Logic
Triangle
Quantum
Right angle
Conformal map
Resultant
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Group action
Presentation of a group
Multiplication sign
Direction (geometry)
Parameter (computer programming)
Rule of inference
Grothendieck topology
Number
Frequency
Group representation
Goodness of fit
Lecture/Conference
Reduction of order
Energy level
Analytic continuation
Field (mathematics)
Subtraction
Descriptive statistics
Perimeter
Series (mathematics)
Product (category theory)
Generating set of a group
Basis (linear algebra)
Line (geometry)
Sequence
Flow separation
Field extension
Commutator
Lattice (order)
Combinatory logic
Chain
Quantum
Object (grammar)
Conformal map
Resultant
Directed graph
48:06
Point (geometry)
Group action
Presentation of a group
State of matter
Multiplication sign
Regular graph
Rule of inference
Group representation
Frequency
Plane (geometry)
Lecture/Conference
Operator (mathematics)
Length
Subtraction
Position operator
Partition (number theory)
Representation theory
Condition number
Standard deviation
Product (category theory)
Spacetime
Rational number
Military base
Basis (linear algebra)
Mortality rate
Bilinear form
Proof theory
Computer animation
Combinatorics
Identical particles
Resultant
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Computer animation
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to be about double algebra it is this a fourleaf phenomena W. held can cost by reduction but it is not the only way the forgery and it is at least 2 more 1 of them we can't take care of them perhaps and to consider here the Jalan minus head and trying to make a sale to find to hear the algebra which commuter these and other it alone that the Commission that it is known that the Vatican responding to Algebra II is also the W some perimeter and these parameters such could see is Walgebra were so who would have came here it is and cable comes here and here at the same number which can be calculated in an and Q it has to be here but they cannot find a way to something yes and so we can get the double algebra by this week and here we get dressed the same object but he used to work now no necessary lit into Germany this level here and we get something so by this way and this is a sort of around .period it sinks and a weekend if would define "quotation mark revising its and then made the analytic continuation by these and even gives me the same object years and and 1 more thing that take if we got our little to this Consent little bit differently we can find and then the corresponding cassette is also Walgebra but a different kind because we can't take you the algebra GAA and and minus 1 and then make up for their bemused tone in the direction of a similar kind for the as a result it gives us the percentage of the same object as the result of this cases it has some explanation but maybe not for now Our in the full meeting of the foreign to the falling that it is possible to prove but for all is are and the little 1 sinks and the other the fact is that after Quantum the federation in become much more simple and clear and and 1 was sinks that if we I know this I can consider the chain also algebra so let me recall that the EU flyhalf algebra jaded and when I constantly get funds Satan base is what they do I consider see that sequence of some Belgian played Whitaker presentation I restricted to some of those arrested were eligible for Belgium Russia and by doing this I find some specific Have you ever wondered visit we are working so would because they're thinking in these cases about a bridge here which commuter this is commuting therefore the if we apply them this story 2 In a this it this surely cannot be so simple because we only if you believe me that up here is jailed and then I have driven minus 100 lines and so on and that because this disease pretend to be competent of these I can't take a presentation the presentation of the year and the restricted to to the product of the stands this finding it gives real some symptoms such things as basis representation of W algebra and this is a representation of Jr and minus 1 then I can continue these businesses this makes several steps to have and and then they even gives me some counterpart of good fun to Satan the composition and is that rather beat somebody rather similar it's the same data has appeared in different seat the composition of presentation and here we have the products of her presentation John W. eligible the but question of the future of the final rule his of the basis for the review of the use of North different people rescued different statements about where the fair the sinks as it's what you will no no no no no you this is some sense more complicated and stuff but maybe I have on this time they really interesting seeing so that because for W algebra all 4 sites can I have a description so I have the FAA should generate therefore find the importance of I Know What is this and because if I have journalism Hi I know that generators here and it is the question of how to fine inside that generators from this warrant how to make the opposite business so you will have the sound to 500 and my title was the extension of W of conformal field series and what I had in mind tho several sinks action but this is 1 example of that here we have German and head and here have a product of W algebra this product of available Algebra II is a lot of Jared had the viciousness of extension In the problem is how to get there Jay Leno starting from this WE algebra and the more as a standard procedure for all it is doing so standard procedure is we will have a product of token unfulfilled serious for example for a seat from 26 minus and I can extended by adding that some combination of have there are a lot of examples where such kind of machinery is working and this is another special and another complicated case overseas and because my time is almost always this I cannot explain but I can explain the following that win if you are not talking about Universal urban go jailed and that we can take a lot of presentation a jail and head and then the are presentation made independently at highest weeks Warren we can take the 1st simplicity of the locum representation walking representation is what is his lot rector then I backed by German tends to humans was so yes and
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