Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra
type: Item
instance of: scholarly article
title: Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra
zbMATH Open document ID: 0651.17008
DOI: 10.1007/BF01218386
author: Marc Rosso
published in: Communications in Mathematical Physics
publication date: 1988-01-01T00:00:00Z
review text: For any simple complex Lie algebra finite dimensional representations of its quantum \(t\)-analogue (a deformation of its universal enveloping algebra with parameter \(t\)) are proven to be completely reducible if t is not a root of 1. For the irreducible ones there is proven a highest weight theorem and, moreover, they are shown to be deformations of the representations of the initial enveloping algebra. For \(\text{sl}(2)\) the result matches that by \textit{A. V. Odesskii} [An analogue of the Sklyanin algebra, Funkts. Anal. Prilozh. 20, No. 2, 78--79 (1986; Zbl 0606.17013)].
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 81R10
zbMATH DE Number: 4061458
zbMATH Keywords: quantum group
zbMATH Keywords: simple complex Lie algebra
zbMATH Keywords: representations
zbMATH Keywords: deformation
zbMATH Keywords: universal enveloping algebra
zbMATH Keywords: highest weight
Wikidata QID: Q115393854
MaRDI profile type: Publication
cites work: A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
cites work: A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
cites work: Q3762471
description: scientific article; zbMATH DE number 4061458