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Published in 2017 at "Applied Categorical Structures"
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…
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Keywords:
enveloping algebra;
crossed module;
universal enveloping;
crossed modules ... See more keywords
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Published in 2019 at "Journal of Algebra"
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…
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Keywords:
lie rings;
universal enveloping;
color lie;
group algebras ... See more keywords
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Published in 2019 at "Glasgow Mathematical Journal"
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…
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Keywords:
prime ideals;
universal enveloping;
simple modules;
modules universal ... See more keywords
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Published in 2019 at "Communications in Algebra"
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…
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Keywords:
enveloping algebra;
algebra;
universal enveloping;
algebra universal ... See more keywords
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Published in 2021 at "Rocky Mountain Journal of Mathematics"
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.
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Keywords:
enveloping algebras;
universal enveloping;
poisson;
generalized poisson ... See more keywords