Overrings of primitive factors of quantum \(\mathfrak{sl}(2)\)
type: Item
instance of: scholarly article
title: Overrings of primitive factors of quantum \(\mathfrak{sl}(2)\)
zbMATH Open document ID: 0851.17016
DOI: 10.1016/0022-4049(94)00067-S
author: Iwan Praton
published in: Journal of Pure and Applied Algebra
publication date: 1996-11-28T00:00:00Z
review text: This paper classifies completely prime Dixmier algebras over primitive quotients of the quantum enveloping algebra of \(\mathfrak {sl} (2)\); the corresponding classification over the ordinary enveloping algebra of \(\mathfrak {sl} (2)\) looks essentially the same and was done by \textit{S. P. Smith} [J. Pure Appl. Algebra 63, 207-218 (1990; Zbl 0849.17006)] and independently by the author (unpublished). In particular, as in the classical case, every completely prime Dixmier algebra has length at most two as a bimodule (modulo algebraic extensions of the base field) and the length two algebras have half-integral infinitesimal characters as bimodules. Everything is done by explicit calculation and thus one does not need quantized versions of standard structural results on enveloping algebras.
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 17B35
zbMATH DE Number: 810227
zbMATH Keywords: overring of pointwise factors
zbMATH Keywords: primitive quotients
zbMATH Keywords: quantum enveloping algebra
zbMATH Keywords: completely prime Dixmier algebra
zbMATH Keywords: length two algebras
reviewed by: William M. McGovern
MaRDI profile type: Publication
cites work: Moduln mit einem höchsten Gewicht
cites work: Q3328709
cites work: Local finiteness of the adjoint action for quantized enveloping algebras
cites work: On large Dixmier algebras
cites work: Overrings of primitive factor rings of \(U(sl(2,\mathbb{C}))\)
cites work: Q5590089
cites work: Q3710659
description: scientific article; zbMATH DE number 810227