Related papers: (Transposed) Poisson algebra structures on null-fi…
Given a Lie group G whose Lie algebra is endowed with a nondegenerate invariant symmetric bilinear form, we construct a Poisson algebra of continuous functions on a certain open subspace R of the space of representations in G of the…
The nilpotency degree of a relatively free finitely generated associative algebra with the identity $x^n=0$ is studied over finite fields.
We study noncommutative generalizations of such notions of the classical symplectic geometry as degenerate Poisson structure, Poisson submanifold and quotient manifold, symplectic foliation and symplectic leaf for associative Poisson…
We describe $\frac{1}{2}$-derivations, and hence transposed Poisson algebra structures, on Witt type Lie algebras $V(f)$, where $f:\Gamma\to\mathbb C$ is non-trivial and $f(0)=0$. More precisely, if $|f(\Gamma)|\ge 4$, then all the…
In this paper, the so-called differential graded (DG for short) Poisson Hopf algebra is introduced, which can be considered as a natural extension of Poisson Hopf algebras in the differential graded setting. The structures on the universal…
The relations between integrable Poisson algebras with three generators and two-dimensional manifolds are investigated. Poisson algebraic maps are also discussed.
Non-commutative Poisson algebras are the algebras having an associative algebra structure and a Lie algebra structure together with the Leibniz law. Let $P$ be a non-commutative Poisson algebra over some algebraically closed field of…
We introduce the quasi-Poisson enveloping algebra and Poisson enveloping algebra for a non-commutative Poisson algebra. We prove that for a non-commutative Poisson algebra, the category of quasi-Poisson modules is equivalent to the category…
Using the notion of a contravariant derivative, we give some algebraic and geometric characterizations of Poisson algebras associated to the infinitesimal data of Poisson submanifolds. We show that such a class of Poisson algebras provides…
In this paper we extend the almost complex Poisson structures from almost complex manifolds to almost complex Lie algebroids. Examples of such structures are also given and the almost complex Poisson morphisms of almost complex Lie…
In this paper we study the categories of braided categorical associative algebras and braided crossed modules of associative algebras and we relate these structures with the categories of braided categorical Lie algebras and braided crossed…
We study the structure of the category of graded, connected, countable-dimensional, commutative and cocommutative Hopf algebras over a perfect field $k$ of characteristic $p$. Every $p$-torsion object in this category is uniquely a direct…
This paper is devoted to the study of local and 2-local derivations of nullfiliform, filiform and naturally graded quasi-filiform associative algebras. We prove that these algebras as a rule admit local derivations which are not…
Let $A$ be a Poisson Hopf algebra over an algebraically closed field of characteristic zero. If $A$ is finitely generated and connected graded as an algebra and its Poisson bracket is homogeneous of degree $d \geq 0$, then $A$ is…
The aim of this paper is to give a survey of nonassociative Hom-algebra and Hom-superalgebra structures. The main feature of these algebras is that the identities defining the structures are twisted by homomorphisms. We discuss…
First, we review the notion of a Poisson structure on a noncommutative algebra due to Block-Getzler and Xu and introduce a notion of a Hamiltonian vector field on a noncommutative Poisson algebra. Then we describe a Poisson structure on a…
Let $A=F[x,y]$ be the polynomial algebra on two variables $x,y$ over an algebraically closed field $F$ of characteristic zero. Under the Poisson bracket, $A$ is equipped with a natural Lie algebra structure. It is proven that the maximal…
We study post-Lie algebra structures on pairs of Lie algebras $(\mathfrak{g},\mathfrak{n})$, motivated by nil-affine actions of Lie groups. We prove existence results for such structures depending on the interplay of the algebraic…
We study Poisson structures over singular varieties. In this purpose, we consider the Koszul complex associated to the equations of a complete intersection. This complex forms a differential graded algebra which is equivalent to the algebra…
A Poisson algebra is a Lie algebra endowed with a commutative associative product in such a way that the Lie and associative products are compatible via a Leibniz rule. If we part from a Lie color algebra, instead of a Lie algebra, a…