Cohomology and associated deformations for not necessarily co-associative bialgebras
type: Item
instance of: scholarly article
title: Cohomology and associated deformations for not necessarily co-associative bialgebras
zbMATH Open document ID: 0792.16012
DOI: 10.1007/BF00420237
author: Philippe Bonneau
published in: Letters in Mathematical Physics
publication date: 1993-06-29T00:00:00Z
review text: The author, together with \textit{M. Flato} and \textit{G. Pinczon} [ibid. 25, No. 1, 75-84 (1992; Zbl 0761.17006)] introduced a cohomology theory for bialgebras (not necessarily co-associative), and demonstrated the rigidity among bialgebras which model quantum \(sl(2)\). The author develops this cohomology further, and relates it to deformation theory. He constructs a long exact sequence connecting his cohomology and classical Hochschild cohomology spaces. The quasi-co-associative bialgebras form a stable subcategory.
Mathematics Subject Classification ID: 16E40
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 81R50
Mathematics Subject Classification ID: 16S80
zbMATH DE Number: 220475
zbMATH Keywords: cohomology for bialgebras
zbMATH Keywords: rigidity
zbMATH Keywords: quantum sl(2)
zbMATH Keywords: deformation theory
zbMATH Keywords: long exact sequence
zbMATH Keywords: Hochschild cohomology
zbMATH Keywords: quasi-co-associative bialgebras
reviewed by: Earl J. Taft
MaRDI profile type: Publication
cites work: A natural and rigid model of quantum groups
cites work: On the deformation of rings and algebras
description: scientific article; zbMATH DE number 220475