Face algebras. I: A generalization of quantum group theory
type: Item
instance of: scholarly article
title: Face algebras. I: A generalization of quantum group theory
zbMATH Open document ID: 0908.16032
author: Takahiro Hayashi
published in: Journal of the Mathematical Society of Japan
publication date: 1998-10-25T00:00:00Z
review text: Let \(R\) be a commutative separable algebra over a field \(K\). An \(R\)-face algebra \(H\) is a \(K\)-algebra with a coalgebra structure, with connecting axioms involving \(R\). This is a generalization of the idea of a bialgebra. In fact, every \(K\)-bialgebra is a \(K\)-face algebra, and conversely, an \(R\)-face algebra is a \(K\)-bialgebra only if \(R\) is isomorphic to \(K\). As with bialgebras, the category of comodules over an \(R\)-face algebra \(H\) is a monoidal abelian category. In this paper, the author studies elementary properties of face algebras and their comodule categories. By considering additional structures on \(H\) (e.g., an antipode, a universal \(R\)-matrix, a ribbon structure and a *-structure), the comodule category has also some additional structure.
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 18D10
Mathematics Subject Classification ID: 17B37
zbMATH DE Number: 1185901
zbMATH Keywords: bialgebras
zbMATH Keywords: face algebras
zbMATH Keywords: categories of comodules
zbMATH Keywords: monoidal Abelian categories
reviewed by: Earl J. Taft
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/05020293
OpenAlex ID: W2135558420
DOI: 10.2969/JMSJ/05020293
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description: scientific article; zbMATH DE number 1185901