Hopf algebras

Noncommutative symmetric function

In mathematics, the noncommutative symmetric functions form a Hopf algebra NSymm analogous to the Hopf algebra of symmetric functions. The Hopf algebra NSymm was introduced by Israel M. Gelfand, Daniel Krob, Alain Lascoux, Bernard Leclerc, Vladimir Retakh, and Jean-Yves Thibon. It is noncommutative but cocommutative graded Hopf algebra. It has the Hopf algebra of symmetric functions as a quotient, and is a subalgebra of the Hopf algebra of permutations, and is the graded dual of the Hopf algebra of quasisymmetric function. Over the rational numbers it is isomorphic as a Hopf algebra to the universal enveloping algebra of the free Lie algebra on countably many variables. (Wikipedia).

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From playlist Injective, Surjective, and Bijective Functions

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From playlist Determining the Characteristics of Polynomial Functions

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From playlist Injective, Surjective, and Bijective Functions

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From playlist Abstract Algebra

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From playlist Abstract Algebra

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From playlist Find the Asymptotes of Rational Functions

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From playlist Find the Asymptotes of Rational Functions

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From playlist Mathematics

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James Mingo: The infinitesimal Weingarten calculus

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From playlist Spring 2014

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From playlist Noncommutative geometry meets topological recursion 2021

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From playlist Noncommutative geometry meets topological recursion 2021

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From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"

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Related pages

Hopf algebra of permutations | Hopf algebra | Symmetric function | Quasisymmetric function | Universal enveloping algebra | Hasse–Schmidt derivation