Connections between finite dimensional corepresentations of \(U_q(2)\) and \(S_qU(2)\)
type: Item
instance of: scholarly article
title: Connections between finite dimensional corepresentations of \(U_q(2)\) and \(S_qU(2)\)
zbMATH Open document ID: 0952.16043
author: D.-M. Lu
published in: Journal of Algebra
publication date: 2000-10-08T00:00:00Z
review text: Let \(\mathbb{C}\) denote the field of complex numbers and let \(q\) be a non-zero real number. Let \(M_q(2)\) be the space of \(2\times 2\) quantum matrices over \(\mathbb{C}\) and let \(D\in M_q(2)\) denote the quantum determinant. In this paper the finite dimensional corepresentations of the Hopf \(*\)-algebras \(U_q(2)=M_q(2)[D^{-1}]\) and \(S_qU(2)\) are related, where \(S_qU(2)\) is the Hopf \(*\)-algebra constructed by \textit{S.~L.~Woronowicz} [in Publ. Res. Inst. Math. Sci. 23, No. 1, 117-181 (1987; Zbl 0676.46050)]. A new Hopf \(*\)-algebra \(U_q(2)[D^{1/2}]\) is constructed containing \(U_q(2)\) as a Hopf \(*\)-subalgebra, and endowed with an inclusion of Hopf \(*\)-algebras \(S_qU(2)\hookrightarrow U_q(2)[D^{1/2}]\). By this technique, it is shown that any finite dimensional corepresentation of \(U_q(2)\) can be decomposed into those of \(S_qU(2)\) and vice versa. Similar results for finite dimensional coalgebra morphisms are also obtained.
reviewed by: Sonia Natale
Mathematics Subject Classification ID: 16W35
Mathematics Subject Classification ID: 20G42
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 81R50
zbMATH DE Number: 1441798
zbMATH Keywords: Hopf \(*\)-algebras
zbMATH Keywords: quantum groups
zbMATH Keywords: corepresentations
zbMATH Keywords: quantum matrices
MaRDI profile type: Publication
full work available at URL: jabr.1999.8147
OpenAlex ID: W1963796529
cites work: Q3978992
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cites work: Quantum deformations of certain simple modules over enveloping algebras
cites work: Quantum linear groups
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cites work: Compact matrix pseudogroups
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DOI: 10.1006/JABR.1999.8147
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description: scientific article; zbMATH DE number 1441798