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
Color Lie rings and PBW deformations of skew group algebras
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DOI: 10.1016/j.jalgebra.2018.10.012
Abstract: We investigate color Lie rings over finite group algebras and their universal enveloping algebras. We exhibit these universal enveloping algebras as PBW deformations of skew group algebras: Every color Lie ring over a finite group… read more here.
Keywords: lie rings; universal enveloping; color lie; group algebras ... 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
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
Universal enveloping algebras of generalized Poisson–Ore extensions
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DOI: 10.1216/rmj.2021.51.747
Abstract: The main goal of this paper is to study the Poisson universal enveloping algebra of a generalized Poisson–Ore extension. We prove such a Poisson universal enveloping algebra is a twisted tensor product. read more here.
Keywords: enveloping algebras; universal enveloping; poisson; generalized poisson ... See more keywords