A Clifford algebra is a weak Hopf algebra in a suitable symmetric monoidal category.
type: Item
instance of: scholarly article
title: A Clifford algebra is a weak Hopf algebra in a suitable symmetric monoidal category.
zbMATH Open document ID: 1245.16023
author: Daniel Bulacu
published in: Journal of Algebra
publication date: 2011-11-08T00:00:00Z
review text: It is well known that Clifford algebras are group algebras deformed by a 2-cocyle. Furthermore, these algebras, which are not commutative in the usual sense, can be viewed as commutative algebras in certain symmetric monoidal categories of graded vector spaces. In this paper, the author shows that Clifford algebras have also cocommutative coalgebra structures, and consequently commutative and cocommutative weak braided Hopf algebra structures where they lie as commutative algebras. Furthermore, the author proves that all the Cayley-Dickson and Clifford weak braided Hopf algebras are selfdual weak braided Hopf algebras, monoidal Frobenius algebras and monoidal coFrobenius coalgebras within the symmetric monoidal categories of graded vector spaces where they reside.
reviewed by: Liangyun Zhang
Mathematics Subject Classification ID: 16T05
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 18D10
Mathematics Subject Classification ID: 16S80
zbMATH DE Number: 5969527
zbMATH Keywords: Clifford algebras
zbMATH Keywords: weak braided Hopf algebras
zbMATH Keywords: monoidal Frobenius algebras
zbMATH Keywords: periodicity
zbMATH Keywords: symmetric monoidal categories
zbMATH Keywords: cocommutative coalgebras
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2011.02.020
OpenAlex ID: W1972899736
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DOI: 10.1016/J.JALGEBRA.2011.02.020
description: scientific article; zbMATH DE number 5969527