Journal of Lie Theory

no. 2
The Universal Enveloping Algebra U(sl2 sdir V2), its Prime Spectrum and a Classification of its Simple Weight Modules
Journal of Lie Theory, Volume 28 (2018) no. 2, pp. 525-560
\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.
DOI: 10.5802/jolt.1012
Classification: 17B10, 16D25, 16D60, 16D70, 16P50
Keywords: Prime ideal, primitive ideal, weight module, simple module, centralizer 
@article{JOLT_2018_28_2_a9,
     author = {V. V. Bavula and T. Lu},
     title = {The {Universal} {Enveloping} {Algebra} {U(sl\protect\textsubscript{2}} sdir {V\protect\textsubscript{2}),} its {Prime} {Spectrum} and a {Classification} of its {Simple} {Weight} {Modules}},
     journal = {Journal of Lie Theory},
     pages = {525--560},
     year = {2018},
     volume = {28},
     number = {2},
     doi = {10.5802/jolt.1012},
     zbl = {1396.17011},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1012/}
}
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JO  - Journal of Lie Theory
PY  - 2018
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VL  - 28
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ID  - JOLT_2018_28_2_a9
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%0 Journal Article
%A V. V. Bavula
%A T. Lu
%T The Universal Enveloping Algebra U(sl2 sdir V2), its Prime Spectrum and a Classification of its Simple Weight Modules
%J Journal of Lie Theory
%D 2018
%P 525-560
%V 28
%N 2
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.1012/
%R 10.5802/jolt.1012
%F JOLT_2018_28_2_a9
V. V. Bavula; T. Lu. The Universal Enveloping Algebra U(sl2 sdir V2), its Prime Spectrum and a Classification of its Simple Weight Modules. Journal of Lie Theory, Volume 28 (2018) no. 2, pp. 525-560. doi: 10.5802/jolt.1012

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