Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userUniversal Enveloping Algebras of Poisson Superalgebras
68
0
0.0
(
0
)
Authors
Thomas Lamkin
Ask ChatGPT about the research
No Arabic abstract
In this paper, we define and study the universal enveloping algebra of Poisson superalgebras. In particular, a new PBW theorem for Lie-Rinehart superalgebras is proved, leading to a PBW theorem for Poisson superalgebras; we show the universal enveloping algebra of a Poisson Hopf superalgebra (resp. Poisson-Ore extension) is a Hopf superalgebra (resp. iterated Ore extension); and we determine the universal enveloping algebra for examples such as quadratic polynomial Poisson superalgebras and Poisson symmetric superalgebras.
rate research
Read More
We 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. As a supplement, the categorical approach offers new insights into the definitions of Lie-Rinehart algebra morphisms, of modules over Lie-Rinehart algebras and of the infinitesimal gauge algebra of a module.
We determine the skew fields of fractions of the enveloping algebra of the Lie superalgebra osp(1, 2) and of some significant subsu-peralgebras of the Lie superalgebra osp(1, 4). We compare the kinds of skew fields arising from this super context with the Weyl skew fields in the classical Gelfand-Kirillov property.
Universal enveloping algebras of braided m-Lie algebras and PBW theorem are obtained by means of combinatorics on words.
In this paper, we introduce the notions of biderivations and linear commuting maps of Hom-Lie algebras and superalgebras. Then we compute biderivations of the q-deformed W(2,2) algebra, q-deformed Witt algebra and superalgebras by elementary and direct calculations. As an application, linear commuting maps on these algebras are characterized. Also, we introduce the notions of {alpha}-derivations and {alpha}-biderivations for Hom-Lie algebras and superal- gebras, and we establish a close relation between {alpha}-derivations and {alpha}-biderivations. As an illustration, we prove that the q-deformed W(2;2)-algebra, the q-deformed Witt algebra and superalgebra have no nontrivial {alpha}-biderivations. Finally, we present an example of Hom-Lie superalgebras with nontrivial {alpha}-super-derivations and biderivations.
We study universal enveloping Hopf algebras of Lie algebras in the category of weakly complete vector spaces over the real and complex field.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
