THE PRIME IDEALS AND SIMPLE MODULES OF THE UNIVERSAL ENVELOPING ALGEBRA U(𝔟⋉V2)
2019 ◽
Vol 62
(S1)
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pp. S77-S98
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Keyword(s):
AbstractLet 𝔟 be the Borel subalgebra of the Lie algebra 𝔰𝔩2 and V2 be the simple two-dimensional 𝔰𝔩2-module. For the universal enveloping algebra $\[{\cal A}: = U(\gb \ltimes {V_2})\]$ of the semi-direct product 𝔟⋉V2 of Lie algebras, the prime, primitive and maximal spectra are classified. Please approve edit to the sentence “The sets of completely prime…”.The sets of completely prime ideals of $\[{\cal A}\]$ are described. The simple unfaithful $\[{\cal A}\]$-modules are classified and an explicit description of all prime factor algebras of $\[{\cal A}\]$ is given. The following classes of simple U(𝔟⋉V2)-modules are classified: the Whittaker modules, the 𝕂[X]-torsion modules and the 𝕂[E]-torsion modules.
2009 ◽
Vol 20
(03)
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pp. 339-368
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2010 ◽
Vol 82
(3)
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pp. 401-423
Keyword(s):
2013 ◽
Vol 55
(A)
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pp. 195-215
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2018 ◽
Vol 61
(1)
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pp. 16-39
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Keyword(s):
2006 ◽
Vol 16
(04)
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pp. 817-825
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Keyword(s):
2007 ◽
Vol 5
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pp. 195-200
2018 ◽
Vol 2018
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pp. 1-9
2002 ◽
Vol 01
(04)
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pp. 413-424
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Keyword(s):
2009 ◽
Vol 86
(1)
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pp. 1-15
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