Journal of Lie Theory 28 (2018), No. 2, 525--560
Copyright Heldermann Verlag 2018
The Universal Enveloping Algebra U(sl2 sdir V2), 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
[Abstract-pdf]
\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
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