Kleene Stars in Shuffle Algebras

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Kleene Stars in Shuffle Algebras
A (tangled) tale of various (bi-)algebras
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We present some bialgebras and their monoid of characters. We entend, to the case of some rings, the well-known 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 one-parameter groups of characters.
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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 Well-formed 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
Shooting method Algebra Time evolution Spherical cap Physics Nichtlineares Gleichungssystem Musical ensemble Combinatorics
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