Bicommutativity for a class of graded connected Hopf algebras
type: Item
instance of: scholarly article
title: Bicommutativity for a class of graded connected Hopf algebras
zbMATH Open document ID: 0927.16033
DOI: 10.1016/S0022-4049(97)00113-8
author: Mustapha Ameur
author: Saïd Benayadi
author: Chakib Bennis
author: André Roux
published in: Journal of Pure and Applied Algebra
publication date: 1999-12-12T00:00:00Z
review text: The authors show that if \(A\) is a graded connected Hopf algebra over a field of characteristic \(0\) such that all homogeneous elements of strictly positive degree are nilpotent, then \(A\) is commutative and cocommutative. Hence \(A\) is an exterior algebra over the primitive elements. As a consequence, any finite-dimensional graded connected Hopf algebra is commutative and cocommutative. This recovers a result of \textit{H. Hopf} [in Ann. Math., II. Ser. 42, 33-52 (1941; Zbl 0025.09303)].
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 15A75
zbMATH DE Number: 1308302
zbMATH Keywords: bicommutativity
zbMATH Keywords: homogeneous elements
zbMATH Keywords: exterior algebras
zbMATH Keywords: primitive elements
zbMATH Keywords: finite-dimensional graded connected Hopf algebras
reviewed by: Fang Li
MaRDI profile type: Publication
cites work: Q4879966
cites work: Homologie et cohomologie des algèbres de Lie
cites work: Homology of symplectic and orthogonal algebras
cites work: Cyclic homology and the Lie algebra homology of matrices
cites work: On the structure of Hopf algebras
cites work: Q4763802
cites work: Q5590089
full work available at URL: s0022-4049(97)00113-8
OpenAlex ID: W2051878001
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description: scientific article; zbMATH DE number 1308302