Related papers: On identities of $2$-dimensional algebras

In this paper, we classify the finite dimensional irreducible modules for affine BMW algebra over an algebraically closed field with arbitrary characteristic.

We describe differential invariants of infinite-dimensional algebras being equivalence algebras of some classes of PDE and study structure of these algebras.

In recent years, the notion of characteristic polynomial of representations of Lie algebras has been widely studied. This paper provides more properties of these characteristic polynomials. For simple Lie algebras, we characterize the…

In previous work on Clebsch-Gordan coefficients, certain remarkable hexagonal arrays of integers are constructed that display behaviors found in Pascal's Triangle. We explain these behaviors further using the binomial transform and discrete…

The symmetry group structures of two dimensional coupled nonlinear Shr\"{o}dinger equations are considered. We first show that the equations admit infinite dimensional symmetry algebra as well as the corresponding symmetry group depending…

This paper concerns the problem of classifying finite-dimensional real solvable Lie algebras whose derived algebras are of codimension 1 or 2. On the one hand, we present an effective method to classify all $(n+1)$-dimensional real solvable…

Let L be a restricted Lie superalgebra with its 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 characterize L…

We study endomorphisms and derivations of infinite dimensional cyclic Leibniz algebra.

In this papier, by the classical umbral calculus method, we establish identities involving the Appell polynomials and extend some existing identities.

Using adjoint representation of Lie superalgebras, we obtain the matrix form of super-Jacobi and mixed super-Jacobi identities of Lie superbialgebras. By direct calculations of these identities, and use of automorphism supergroups of two…

We prove a universal identity for powers of elements in quadratic algebras, expressing x^m in terms of x and the identity. As a consequence, we obtain a general formula for powers of 2x2 matrices depending only on trace and determinant.…

Finite and Infinite-dimensional representations of symmetry algebras play a significant role in determining the spectral properties of physical Hamiltonians. In this paper, we introduce and apply a practical method to construct infinite…

We observe that a finitely generated algebraic algebra R (over a field) is finite dimensional if and only if the associated graded ring grR is right noetherian, if and only if grR has right Krull dimension, if and only if grR satisfies a…

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…

In this paper, we obtain a general formula for the characteristic polynomial of a finitely dimensional representation of Lie algebra $\mathfrak{sl}(2, \C )$ and the form for these characteristic polynomials, and prove there is one to one…

We associate an square to any two dimensional evolution algebra. This geometric object is uniquely determined, does not depend on the basis and describes the structure and the behaviour of the algebra. We determine the identities of degrees…

In 1970 Vaughan-Lee established that over an infinite field of characteristic two the ideal T[gl(2)] of all polynomial identities for the Lie algebra gl(2) is not finitely generated as a T-ideal. But a generating set for this ideal of…

An algebra is said to be a unary Leibniz algebra if every one-generated subalgebra is a Leibniz algebra. An algebra is said to be a binary Leibniz algebra if every two-generated subalgebra is a Leibniz algebra. We give characterizations of…

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…

We give a full classification, up to equivalence, of finite-dimensional graded division algebras over the field of real numbers. The grading group is any abelian group.