Finite dimensional modules for the \(q\)-tetrahedron algebra
type: Item
instance of: scholarly article
title: Finite dimensional modules for the \(q\)-tetrahedron algebra
zbMATH Open document ID: 1232.17026
author: Kei Miki
published in: Osaka Journal of Mathematics
publication date: 2010-08-13T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.ojm/1277298918
review text: Let \(B\) the complex Laurent polynomial algebra in one variable \(t\) and \(A\) the localisation of \(B\) by \(t-1\). The thetrahedron algebra \(\boxtimes\) is the complex Lie algebra \(sl_2\otimes A\) with the Lie bracketing \[ [u\otimes a,v\otimes b]= [u,v]\otimes ab. \] The Lie algebra \(L(sl_2)\) is the Lie subalgebra \(sl_2\otimes B\) in \(sl_2\otimes A\). In 2007 \textit{T. Ito} and \textit{P. Terwilliger} [Commun. Algebra 35, No. 11, 3415--3439 (2007; Zbl 1133.17011)] introduced \(q\)-analog \(\boxtimes_q\) of the algebra \(\boxtimes\). The aim of the paper is establish relations between finite dimensional modules over \(\boxtimes_q\) and finite dimensional modules over \(U_q(L(sl_2)).\) There relations modify similar relations between modules over \(\boxtimes\) and over the Onsager algebra.
reviewed by: Vyacheslav A. Artamonov
Mathematics Subject Classification ID: 17B37
zbMATH DE Number: 5770027
zbMATH Keywords: Lie algebras
zbMATH Keywords: quantization
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5770027