相关论文: Power-associative evolution algebras
In this paper we give an explicit description of primitive central idempotents of rational group algebras of finite abelian groups using long presentation, and determine their Wedderburn decompositions.
We classify nilpotent associative algebras of dimensions up to 4 over any field. This is done by constructing the nilpotent associative algebras as central extensions of algebras of smaller dimension, analogous to methods known for…
In this paper, bimodules over Hom-Jordan algebras and the ones over Hom-alternative algebras are defined. It is shown that bimodules over Jordan and alternative algebras are twisted into bimodules over Hom-Jordan and Hom-alternative…
We develop the notion of deformations using a valuation ring as ring of coefficients. This permits to consider in particular the classical Gerstenhaber deformations of associative or Lie algebras as infinitesimal deformations and to solve…
In this article we study algebraic structures of function spaces defined by graphs and state spaces equipped with Gibbs measures by associating evolution algebras. We give a constructive description of associating evolution algebras to the…
The aim of this paper is to offer an overview of the most important applications of Jordan structures inside mathematics and also to physics, up-dated references being included. For a more detailed treatment of this topic see - especially -…
This note is an expanded and updated version of our entry with the same title for the 2006 Encyclopedia of Mathematical Physics. We give a brief overview of graded Poisson algebras, their main properties and their main applications, in the…
The goal of this paper is to present an algebraic approach to the basic results of the theory of linear recurrence relations. This approach is based on the ideas from the theory of representations of one endomorphisms (a special case of…
We study the concept of extended derivations of algebras which expands diverse definitions of generalized derivations given in the literature. We concentrate on the family of the anti-commutative algebras and classify such spaces of…
The algebraic and geometric classification of all complex $3$-dimensional transposed Poisson algebras is obtained. Also, we discuss strong special $3$-dimensional transposed Poisson algebras.
We classify, up to isomorphism and up to equivalence, involutions on graded-division finite-dimensional simple real (associative) algebras, when the grading group is abelian.
The algebraic and geometric classifications of complex $3$-dimensional noncommutative Jordan superalgebras are given. In particular, we obtain the algebraic and geometric classification of $3$-dimensional Kokoris and standard superalgebras,…
The present work is devoted to the extension of some general properties of automorphisms and derivations which are known for Lie algebras to finite dimensional complex Leibniz algebras. The analogues of the Jordan-Chevalley decomposition…
Lie conformal algebras appear in the theory of vertex algebras. Their relation is similar to that of Lie algebras and their universal enveloping algebras. Associative conformal algebras play a role in conformal representation theory. We…
We study associative multiplications in semi-simple associative algebras over C compatible with the usual one or, in other words, linear deformations of semi-simple associative algebras over C. It turns out that these deformations are in…
An algebraic classification of complex $5$-dimensional nilpotent commutative $\mathfrak{CD}$-algebras is given. This classification is based on an algebraic classification of complex $5$-dimensional nilpotent Jordan algebras.
These notes present an introduction to an analytic version of deformation quantization. The central point is to study algebras of physical observables and their irreducible representations. In classical mechanics one deals with real Poisson…
Natural linear and coalgebra transformations of tensor algebras are studied. The representations of certain combinatorial groups are given. These representations are connected to natural transformations of tensor algebras and to the groups…
We give a geometric classification of $n$-dimensional nilpotent, commutative nilpotent and anticommutative nilpotent algebras. We prove that the corresponding geometric varieties are irreducible, find their dimensions and describe explicit…
Weighted Rota-Baxter Jacobi-Jordan algebras and their representations are studied. Moreover, we consider weighted Rota-Baxter paired operators that are related to weighted Rota-Baxter Jacobi-Jordan algebras together with their…