Related papers: Algebras with Laurent polynomial identity
The notion of block divisibility naturally leads one to introduce unitary cyclotomic polynomials. We formulate some basic properties of unitary cyclotomic polynomials and study how they are connected with cyclotomic, inclusion-exclusion and…
In this paper we look into the structure of finite-dimensional graded superalgebras of various types such as associative, Lie and Jordan over an algebraically closed field of characteristic zero.
Inductive algebras for a compact group are self-adjoint
We give several families of polynomials which are related by Eulerian summation operators. They satisfy interesting combinatorial properties like being integer-valued at integral points. This involves nearby-symmetries and a recursion for…
Let L be a restricted Lie superalgebra with its restricted enveloping algebra u(L) over a field F of characteristic p>2. A polynomial identity is called non-matrix if it is not satisfied by the algebra of 2\times 2 matrices over F. We…
Isoclinism of Lie superalgebras has been defined and studied currently. In this article it is shown that for finite dimensional Lie superalgebras of same dimension, the notation of isoclinism and isomorphism are equivalent. Furthermore we…
The present paper is devoted to the description of finite-dimensional semisimple Leibniz algebras over complex numbers, their derivations and automorphisms.
We extend the classification of solvable Lie algebras with abelian nilradicals to classify solvable Leibniz algebras which are one dimensional extensions of an abelian nilradicals.
In the paper, I consider properties and mappings of free algebra with unit. I consider also conjugation of free algebra with unit.
Numerical characteristics of polynomial identities of left nilpotent algebras are examined. Previously, we came up with a construction which, given an infinite binary word, allowed us to build a two-step left nilpotent algebra with…
The aim of this short note is to show how can be derived from the properties of fundamental interpolation polynomials some nice identities.
We describe a family of polynomials discovered via a particular recursion relation, which have connections to Chebyshev polynomials of the first and the second kind, and the polynomial version of Pell's equation. Many of their properties…
We obtain a lifting property for finite quotients of algebraic groups, and applications to the structure of these groups.
In this paper, we study compatible Leibniz algebras. We characterize compatible Leibniz algebras in terms of Maurer-Cartan elements of a suitable differential graded Lie algebra. We define a cohomology theory of compatible Leibniz algebras…
We establish some results about large restricted Lie algebras similar to those known in the Group Theory. As an application we use this group-theoretic approach to produce some examples of restricted as well as ordinary Lie algebras which…
We announce numerous new results in the theory of orthogonal polynomials on the unit circle.
We complete the description of group gradings on finite-dimensional incidence algebras. Moreover, we classify the finite-dimensional graded algebras that can be realized as incidence algebras endowed with a group grading.
The G\"ollnitz-Gordon-Andrews identities generalize the partition identities discovered independently by H. G\"ollnitz and B. Gordon. In this article, we present a commutative algebra proof of the G\"ollnitz-Gordon-Andrews identities. More…
In this paper we consider the weighted q-Bernoulli numbers and polynomials which are differnt type of Carlitz's q-Bernoulli numbers and polynomials. From these numbers and polynomials, we derive some interesting formulaes and identities.
The main aim of this paper is to classify the distinct multiplicative Lie algebra structures (up to isomorphism) on a given group. We also see that for a given group $G$, every homomorphism from the non-abelian exterior square $G \wedge G$…