A bicovariant differential algebra of a quantum group
type: Item
instance of: scholarly article
title: A bicovariant differential algebra of a quantum group
zbMATH Open document ID: 0937.16047
DOI: 10.1016/S0034-4877(99)80040-8
author: O. Radko
published in: Reports on Mathematical Physics
publication date: 2000-06-04T00:00:00Z
review text: In the framework of the general concept of quantum (\(q\)-deformed) Lie groups it is shown in which way the Hopf-algebraic structure of the noncommutative bicovariant differential calculus (1989, Woronowicz) can be used to build an associative noncommutative bicovariant algebra. Such an algebra on \(\text{GL}_q(N)\) involving the quantum analogues of the classical coordinate functions on Lie groups, differential forms, Lie derivatives along vector fields and inner derivations on Hopf algebras is explicitly constructed. As distinct from known investigations, a direct application is made to the Woronowicz differential complex of the cross-products of mutually dual Hopf algebras providing the bicovariance of the noncommutative differential algebra under consideration. A correspondence with classical differential calculus as well as the (co)module properties of the obtained bicovariant algebra on \(\text{GL}_q(N)\) are discussed. The present paper gives a reformulation of previous more extended work (1997, Radko, Vladimirov).
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 58B32
Mathematics Subject Classification ID: 81R50
Mathematics Subject Classification ID: 46L87
Mathematics Subject Classification ID: 17B81
zbMATH DE Number: 1342959
zbMATH Keywords: quantum Lie groups
zbMATH Keywords: quantum groups
zbMATH Keywords: bicovariant differential calculus
zbMATH Keywords: Lie derivatives
zbMATH Keywords: inner derivations
zbMATH Keywords: cross-products
zbMATH Keywords: Hopf algebras
reviewed by: A. A. Bogush
MaRDI profile type: Publication
cites work: Differential calculus on compact matrix pseudogroups (quantum groups)
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cites work: On the algebraic structure of differential calculus on quantum groups
description: scientific article; zbMATH DE number 1342959