
Journal of Lie Theory 28 (2018), No. 2, 525560 Copyright Heldermann Verlag 2018 The Universal Enveloping Algebra U(sl_{2} sdir V_{2}), its Prime Spectrum and a Classification of its Simple Weight Modules Vladimir V. Bavula Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, England v.bavula@sheffield.ac.uk Tao Lu School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, P. R. China lutao@hqu.edu.cn [Abstractpdf] \def\l{{\frak l}} \def\s{{\frak s}} \def\sdir#1{\hbox{$\mathrel\times{\hskip 4.3pt {\vrule height 4.0 pt depth 0 pt}}\hskip 2pt_{#1}$}} For the enveloping algebra $A$ of the Lie algebra $\s\l_2\sdir{}V_2$, explicit descriptions of its prime, primitive, completely prime and maximal spectra are given. A classification of simple weight $\s\l_2\sdir{}V_2$modules is given. Generators and defining relations are found for the centralizer $C_A(H)$ in $A$ of the Cartan element $H$ of $\s\l_2\sdir{}V_2 $. Explicit descriptions of the prime, primitive, completely prime and maximal spectra of $C_A(H)$ are given. Simple $C_A(H)$modules are classified. Keywords: Prime ideal, primitive ideal, weight module, simple module, centralizer. MSC: 17B10, 16D25, 16D60, 16D70, 16P50 [ Fulltextpdf (441 KB)] for subscribers only. 