Geodesic
The Universal Enveloping Algebra U(sl2 sdir V2), its Prime Spectrum and a Classification of its Simple Weight Modules
Vladimir V. Bavula1 ; Tao Lu2
1Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, England
2School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, P. R. China
Journal of Lie Theory, Tome 28 (2018) no. 2, pp. 525-560

Voir la notice de l'article provenant de la source Heldermann Verlag

\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.
Classification : 17B10, 16D25, 16D60, 16D70, 16P50
Mots-clés : Prime ideal, primitive ideal, weight module, simple module, centralizer

Vladimir V. Bavula  1   ; Tao Lu  2

1 Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, England
2 School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, P. R. China 
Vladimir V. Bavula; Tao Lu. The Universal Enveloping Algebra U(sl2 sdir V2), its Prime Spectrum and a Classification of its Simple Weight Modules. Journal of Lie Theory, Tome 28 (2018) no. 2, pp. 525-560. http://geodesic.mathdoc.fr/item/JOLT_2018_28_2_a9/
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     author = {Vladimir V. Bavula and Tao 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},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2018_28_2_a9/}
}
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