Construction of cyclic representations of quantum algebras at \(q^ p=1\) from their regular representations
type: Item
instance of: scholarly article
title: Construction of cyclic representations of quantum algebras at \(q^ p=1\) from their regular representations
zbMATH Open document ID: 0759.17006
DOI: 10.1007/BF00398400
published in: Letters in Mathematical Physics
publication date: 1993-01-17T00:00:00Z
review text: Let \(L\) be a finite dimensional simple Lie algebra, and \(U_ qL\) the quantum algebra associated with \(L\), where \(q\) is the primitive \(p\)-th root of unity and \(p\) is an odd prime. In the present paper the authors construct the cyclic representation of maximal dimension for the quantum algebra \(U_ qsl(2)\), which is just that defined by De Concini and Kac. They then generalize the method of general \(U_ qL\), and construct the cyclic representation of maximal dimension for \(U_ qL\) from its regular representation. Furthermore, the cyclic representation for \(U_ qsl(3)\) is also constructed. This work is a continuation of several mathematicians' work in this direction.
reviewed by: Ye Jiachen
Mathematics Subject Classification ID: 17B37
zbMATH DE Number: 97829
zbMATH Keywords: cyclic representation
zbMATH Keywords: quantum algebra
zbMATH Keywords: regular representation
author: Hong-Chen Fu
author: Molin Ge
describes a project that uses: GeM
MaRDI profile type: Publication
cites work: A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
cites work: Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra
cites work: Irreducible representations of the quantum analogue of SU(2)
cites work: Structure of regular representation of quantum universal enveloping algebra SLq(2) with qp=1*
cites work: Q3972941
cites work: Cyclic boson algebra and q-boson realizations of cyclic representations of the quantum algebra slq(3)
cites work: The q-boson realization of parametrized cyclic representations of quantum algebras at q p = 1
cites work: The cyclic representations of the quantum superalgebra \(U_ q\)osp(2,1) with \(q\) a root of unity
cites work: The universal R-matrix for \(U_ qsl(3)\) and beyond!
full work available at URL: https://doi.org/10.1007/bf00398400
OpenAlex ID: W1993576068
description: scientific article; zbMATH DE number 97829