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Vertex algebras, Kac-Moody algebras, and the Monster. [PDF]
Proc Natl Acad Sci U S A, 1986 Borcherds RE.
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Young-Capelli symmetrizers in superalgebras. [PDF]
Proc Natl Acad Sci U S A, 1989 Brini A, Teolis AG.
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Indefinite intertwining operators. [PDF]
Proc Natl Acad Sci U S A, 1984 Baldoni-Silva MW, Knapp AW.
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Lectures on Duflo isomorphisms in Lie algebra and complex geometry
, 2011 D. Calaque, C. Rossi
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Quantized universal enveloping superalgebra of type Q and a super-extension of the Hecke algebra
Letters in Mathematical Physics, 1992 The ``strange'' Lie superalgebra \(q(n)\) is unfriendly in several ways: The Cartan subalgebra is not purely even, there is no invariant bilinear form and no quadratic Casimir operator. In some other respects the algebra has properties analogous to those of the general linear algebra \(\text{gl}(n)\).
Grigori Olshanski
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Koszul Duality for Semidirect Products and Generalized Takiff Algebras
Algebras and Representation Theory, 2015We obtain Koszul-type dualities for categories of graded modules over a graded associative algebra which can be realized as the semidirect product of a bialgebra coinciding with its degree zero part and a graded module algebra for the latter.
Jacob Greenstein, V. Mazorchuk
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Automorphisms of simple quotients of the Poisson and universal enveloping algebras of sl2
Journal of Algebra and its Applications, 2022Let [Formula: see text] be the Poisson enveloping algebra of the Lie algebra [Formula: see text] over an algebraically closed field [Formula: see text] of characteristic zero. The quotient algebras [Formula: see text] [Formula: see text], where [Formula:
A. Naurazbekova, U. Umirbaev
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Universal Enveloping Algebras of Lie–Rinehart Algebras as a Left Adjoint Functor
Mediterranean Journal of Mathematics, 2021We prove how the universal enveloping algebra constructions for Lie–Rinehart algebras and anchored Lie algebras are naturally left adjoint functors. This provides a conceptual motivation for the universal properties these constructions satisfy.
P. Saracco
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Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2021
We describe the centers of the universal enveloping algebras of nilpotent Lie algebras of dimension at most six over fields of prime characteristic. If the characteristic is not smaller than the nilpontency class, then the center is the integral closure ...
Vanderlei Lopes de Jesus +1 more
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We describe the centers of the universal enveloping algebras of nilpotent Lie algebras of dimension at most six over fields of prime characteristic. If the characteristic is not smaller than the nilpontency class, then the center is the integral closure ...
Vanderlei Lopes de Jesus +1 more
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Universal enveloping of (modified) λ-differential Lie algebras
Linear and multilinear algebra, 2020We introduce a new operator – a modified λ-differential operator – from a usual differential operator. We construct the free (modified) λ-differential -algebra on a (modified) differential -module, and apply it to erect the universal enveloping (modified)
Xiao-song Peng +3 more
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