Related papers: Partially Commutative Groups And Lie Algebras
In this paper, we study partial actions of groups on $R$-algebras, where $R$ is a commutative ring. We describe the partial actions of groups on the indecomposable algebras with enveloping actions. Then we work on algebras that can be…
In this paper we investigate the problem of which Lie algebras appear as the derived algebra of a Lie algebra. We present new results that further develop this study and address two questions raised in a paper concerned with the…
We introduce the notion of the partial group algebra with projections and relations and show that this C*-algebra is a partial crossed product. Examples of partial group algebras with projections and relations are the Cuntz-Krieger algebras…
We consider the natural Lie algebra structure on the (associative) group algebra of a finite group $G$, and show that the Lie subalgebras associated to natural involutive antiautomorphisms of this group algebra are reductive ones. We give a…
The aim of this paper is to introduce and study Lie algebras and Lie groups over noncommutative rings. For any Lie algebra $\gg$ sitting inside an associative algebra $A$ and any associative algebra $\FF$ we introduce and study the algebra…
The main aim of this paper is to determine the multiplicative lie algebra structures on the semi-direct product of an abelian group with a group under certain conditions.
We study so called regular Lie algebras, i.e. Lie algebras in which each nonzero element is regular. We make a connection with an open problem whether any element of reduced trace zero in a simple associative algebra is a commutator.
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…
These notes deal with a few aspects of Lie algebras and Lie groups, including some matters related to exponentiation.
In this work, we give a survey of recent developments in the theory of partial actions of groups and Hopf algebras.
In this work, we prove that partially commutative, partially commutative metabelian, or partially commutative nilpotent Lie algebra splits into the direct sum of two subalgebras if and only if the completion of the defining graph of this…
In this note we introduce and study the almost commuting varieties for the symplectic Lie algebras.
It is explicitly shown how the Lie algebras can be associated with the analytic Moufang loops. The resulting Lie algebra commutation relations are well known from the theory of alternative algebras and can be seen as a preliminary step to…
The Lie algebras over the algebra of dual numbers are introduced and investigated.
This is a survey on extended affine Lie algebras and related types of Lie algebras, which generalize affine Lie algebras.
We give a unified description of morphisms and comorphisms of Lie pseudoalgebras, showing that the both types of morphisms can be regarded as subalgebras of a Lie pseudoalgebra, called the $\psi$-sum. We also provide similar descriptions…
We introduce the notion of Gamma-Lie bialgebra, where Gamma is a group. These objects give rise to cocommutative co-Poisson algebras, for which we construct quantization functors. This enlarges the class of co-Poisson algebras for which a…
In this paper, the complete description of centralizers of elements in partially commutative Lie algebras is obtained. The description is given explicitly in the terms of generators.
In this paper, we introduce a novel generalization of the classical property of algebras known as "being alternative," which we term "partially alternative." This new concept broadens the scope of alternative algebras, offering a fresh…
Inspired by the commutator and anticommutator algebras derived from algebras graded by groups, we introduce noncommutatively graded algebras. We generalize various classical graded results to the noncommutatively graded situation concerning…