Color Lie superalgebras and Hopf algebras
type: Item
instance of: scholarly article
title: Color Lie superalgebras and Hopf algebras
zbMATH Open document ID: 0856.16039
DOI: 10.1007/BF00739407
author: A. N. Koryukin
published in: Algebra and Logic
publication date: 1997-01-09T00:00:00Z
full work available at URL: https://eudml.org/doc/187736
review text: The author is concerned with extending the theorem asserting the equivalence of the category of primitively generated Hopf algebras to the category of (restricted) Lie algebras [cf. \textit{J. W. Milnor} and \textit{J. C. Moore}, Ann. Math., II. Ser. 81, 211-264 (1965; Zbl 0163.28202)] to the case of colour Lie superalgebras. Here the primitively generated Hopf algebra becomes a Hopf algebra \(H\) whose semigroup (i.e. grouplike) elements form an abelian group \(G=G(H)\), while \(H\) is generated by its relatively primitive elements (i.e. satisfying \(\Delta(\delta)=\delta\otimes 1+s\otimes\delta\), for some \(s\in G(H)\)), which `supercommute' with the elements of \(G\). The notions of colour Lie superalgebra and \(\varepsilon\)-bialgebra are carefully explained and the proof proceeds by an induction on the natural filtration.
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 17B70
Mathematics Subject Classification ID: 16D90
zbMATH DE Number: 907279
zbMATH Keywords: supercommuting elements
zbMATH Keywords: grouplike elements
zbMATH Keywords: category of primitively generated Hopf algebras
zbMATH Keywords: colour Lie superalgebras
Wikidata QID: Q115394935
reviewed by: Paul M. Cohn
MaRDI profile type: Publication
cites work: On the structure of Hopf algebras
cites work: Properness of Lie Algebras and Enveloping Algebras. I
cites work: The theory of Lie superalgebras. An introduction
cites work: Q4002121
cites work: Generalized Lie algebras
cites work: Free Hopf algebras generated by coalgebras
cites work: Q3909162
description: scientific article; zbMATH DE number 907279