A Natural Extension of the Universal Enveloping Algebra Functor to Crossed Modules of Leibniz Algebras
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DOI: 10.1007/s10485-016-9472-9
Abstract: The universal enveloping algebra functor between Leibniz and associative algebras defined by Loday and Pirashvili is extended to crossed modules. We prove that the universal enveloping crossed module of algebras of a crossed module of… read more here.
Keywords: enveloping algebra; crossed module; universal enveloping; crossed modules ... See more keywords
THE PRIME IDEALS AND SIMPLE MODULES OF THE UNIVERSAL ENVELOPING ALGEBRA U(𝔟⋉V2)
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DOI: 10.1017/s0017089519000302
Abstract: Abstract Let 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… read more here.
Keywords: prime ideals; universal enveloping; simple modules; modules universal ... See more keywords
Prime ideals of the enveloping algebra of the Euclidean algebra and a classification of its simple weight modules
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DOI: 10.1063/1.4973378
Abstract: A classification of the simple weight modules is given for the (6-dimensional) Euclidean Lie algebra ????(3) = ????????2⋉V3. As an intermediate step, a classification of all simple modules is given for the centralizer C of… read more here.
Keywords: classification simple; enveloping algebra; simple weight; classification ... See more keywords
Presenting q-Schur algebras as quotients of the quantized enveloping algebra of sln
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DOI: 10.1063/1.5095513
Abstract: In the work of Doty and Giaquinto [Int. Math. Res. Not. 36, 1907 (2002)] and Du and Parshall [Trans. Am. Math. Soc. 355, 1593 (2003)], the presentations of q-Schur algebra as a quotient of quantum… read more here.
Keywords: enveloping algebra; algebra; schur algebra; quantized enveloping ... See more keywords
The universal enveloping algebra of and the Racah algebra
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DOI: 10.1080/00927872.2019.1670199
Abstract: Abstract Let denote a field with The Racah algebra is the unital associative -algebra defined by generators and relations in the following way. The generators are A, B, C, D. The relations assert that and… read more here.
Keywords: enveloping algebra; algebra; universal enveloping; algebra universal ... See more keywords