The weight decomposition of Hopf algebras. (La décomposition en poids des algèbres de Hopf.) (French) Zbl 0795.16028

Patras, Frédéric

Ann. Inst. Fourier 43, No. 4, 1067-1087 (1993).

Let \(H\) be a connected Hopf algebra. The convolution powers of the identity endomorphism of \(H\) have nice algebraic properties which can be described using the logarithm in the convolution algebra of linear endomorphisms of \(H\). Those operations provide \(H\) with a weight- decomposition.

Reviewer: F.Patras (Nice)

MSC:

16W30	Hopf algebras (associative rings and algebras) (MSC2000)
17B70	Graded Lie (super)algebras
55P45	\(H\)-spaces and duals
17B01	Identities, free Lie (super)algebras
17B10	Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)

Keywords:

free Lie algebra; connected Hopf algebra; convolution powers; logarithm; convolution algebra; linear endomorphisms; weight-decomposition

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