Rigidity of maps from Hopf algebras to group algebras
type: Item
instance of: scholarly article
title: Rigidity of maps from Hopf algebras to group algebras
zbMATH Open document ID: 0649.16006
DOI: 10.1016/0021-8693(88)90044-0
author: S. H. Smith
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: It is well-known in the theory of algebraic groups that one cannot deform maps from a diagonalizable group to a linear algebraic group except trivially, i.e., by conjugation with inner automorphisms of the target. This note gives a noncommutative analogue of this result in which linear algebraic groups are replaced by finitely generated bialgebras and diagonal groups are replaced by cancellative monoid algebras. The underlying field must be algebraically closed of characteristic zero. The arguments are Hopf-algebra theoretic with some differential algebra.
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 20M25
Mathematics Subject Classification ID: 16E40
zbMATH DE Number: 4059604
zbMATH Keywords: rigidity
zbMATH Keywords: finitely generated bialgebras
zbMATH Keywords: cancellative monoid algebras
zbMATH Keywords: Hopf-algebra
reviewed by: Earl J. Taft
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90044-0
OpenAlex ID: W2029887509
cites work: Differential function fields and moduli of algebraic varieties
cites work: Q5614410
cites work: Q5680222
cites work: Q5590089
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description: scientific article; zbMATH DE number 4059604