Related papers: Left-symmetric Algebras From Linear Functions
Hidden symmetries, described by higher order in momenta integrals of motion that generate nonlinear algebras, are explored at the level of classical and quantum mechanics in a variety of physical systems related to conformal and…
In this paper, we study three classes of subvarieties inside the variety of left-symmetric algebras. We show that these subvarieties are naturally related to some well-known varieties, such as alternative, assosymmetric and Zinbiel…
In this paper we give the complete classification of $5$-dimensional complex solvable symmetric Leibniz algebras.
Leibniz algebras are certain generalization of Lie algebras. In this paper we give classification of non-Lie solvable (left) Leibniz algebras of dimension $\leq 8$ with one dimensional derived subalgebra. We use the canonical forms for the…
We describe generating functions for several important families of classical symmetric functions and shifted Schur functions. The approach is originated from vertex operator realization of symmetric functions and offers a unified method to…
Multiplicative left Hom-Leibniz algebras have natural Hom-Lie-Yamaguti structure.
Enveloping algebras of Hom-Lie and Hom-Leibniz algebras are constructed.
Motivated by a question of Rota, this paper studies the relationship between Rota--Baxter algebras and symmetric related functions. The starting point is the fact that the space of quasi-symmetric functions is spanned by monomial…
Let $L$ be an algebra over a field $F$ with the binary operations $+$ and $[,]$. Then $L$ is called a left Leibniz algebra if it satisfies the left Leibniz identity: $[[a,b],c]=[a,[b,c]]-[b,[a,c]]$ for all elements $a,b,c\in L$. A linear…
The purpose of this paper is to introduce an algebraic cohomology and formal deformation theory of left alternative algebras. Connections to some other algebraic structures are given also.
Jacobi's elliptic functions have been constructed from a deformed Lie algebra. The generators of the algebra have been obtained from a bi-orthogonal system. The deformation parameter resembles the modulus of the relevant elliptic functions.
Dekimpe and Ongenae constructed infinitely many pairwise non-isomorphic complete left-symmetric structures on $\mathbb{R}^n$ for $n\geq 6$. In this paper, we construct a family of complete left-symmetric structures on the cotangent Lie…
A Lie superalgebra is attached to any finite-dimensional J-ternary algebra over an algebraically closed field of characteristic 3, using a process of semisimplification via tensor categories. Some of the exceptional simple Lie algebras,…
All subalgebras, idempotents, left(right) ideals and left quasi-units of two-dimensional algebras are described. Classification of algebras with given number of subalgebras, left(right) ideals are provided. In particular, a list of…
Every (left) linear function on a subspace of a finite-dimensional vector space over a (skew) field can be extended to a (left) linear function on the whole space. This paper explores the extent to what this basic fact of linear algebra is…
The structure of classical non-linear $\cw$ algebras closing on rational functions is analyzed both for the ordinary and the supersymmetric case. Such algebras appear as a result of a coset construction. Their relevance to physical…
The fundamental symmetries in gravity and gauge theories, formulated using differential forms, are gauge transformations and diffeomorphisms. These symmetries act in distinct ways on different dynamical fields. Yet, the commutator of these…
In this paper, we study admissible $\omega$-left-symmetric algebraic structures on $\omega$-Lie algebras over the complex numbers field $\mathbb C$. Based on the classification of $\omega$-Lie algebras, we prove that any perfect…
In this paper, we introduce the concepts of endomorphism operator, left averaging operator, differential operator and Rota-Baxter Operator, and we construct examples of these linear maps on associative algebras with a left identity, a…
We develop here a concept of deformed algebras through three examples and an application. Deformed algebras are obtained from a fixed algebra by deformation along a family of indexes, through formal series. We show how the example of…