Related papers: Associative nil-algebras over finite fields
The class of minimal non-elementary Lie algebras over a field F are studied. These are classified when F is algebraically closed and of characteristic different from 2,3. The solvable algebras in this class are also characterised over any…
We study the existence of free subalgebras in division algebras, and prove the following general result: if $A$ is a noetherian domain which is countably generated over an uncountable algebraically closed field $k$ of characteristic 0, then…
We provide a clarification of the classification of two-dimensional algebras over an arbitrary base field. Using this clarification, we determine the number of non-isomorphic two-dimensional algebras over a finite field.
An algebra is finitely related (or has finite degree) if its term functions are determined by some finite set of finitary relations. Nilpotent monoids built from words, via Rees quotients of free monoids, have been used to exhibit many…
An algebra with identities $(a,b,c)=(a,c,b)=(b,a,c)$ is called {\it assosymmetric}, where $(x,y,z)=(xy)z-x(yz)$ is associator. We study $S_n$-module, $A_n$-module and $GL_n$-module structures of free assosymmetric algebra.
We give some examples of non-complete invariant affine connections on nilpotent and filiform Lie groups. This permits to describe non-nilpotent faithful representations on the model of filiform n-dimensional Lie algebras and, in particular,…
Let $A$ and $B$ be finite-dimensional simple algebras with arbitrary signature over an algebraically closed field. Suppose $A$ and $B$ are graded by a semigroup $S$ so that the graded identitical relations of $A$ are the same as those of…
In this paper, we study Novikov algebras satisfying nontrivial identities. We show that a Novikov algebra over a field of zero characteristic that satisfies a nontrivial identity satisfies some unexpected "universal" identities, in…
This paper is a contribution to the development of the non associative algebras theory. More precisely, this work deals with the classification of the complex 4-dimensional Leibniz algebras. Note that the classification of 4-dimensional…
We describe all irreducible conformal subalgebras of Cend_N. The classification of simple and semisimple associative conformal algebras with finite faithful representation follows from this description.
In this paper, for a given finitely generated algebra (an algebraic structure with arbitrary operations and no predicates) A we study finitely generated limit algebras of A, approaching them via model theory and algebraic geometry. Along…
We describe solvable Leibniz algebras whose nilradical is a quasi-filiform Leibniz algebra of maximum length.
The class of finitely presented algebras over a field $K$ with a set of generators $a_{1},..., a_{n}$ and defined by homogeneous relations of the form $a_{1}a_{2}... a_{n} =a_{\sigma (a)} a_{\sigma (2)} ... a_{\sigma (n)}$, where $\sigma$…
The classification, both up to isomorphism or up to equivalence, of the gradings on a finite dimensional nonassociative algebra A over an algebraically closed field F, such that its group scheme of automorphisms is smooth, is shown to be…
A finite-dimensional Lie algebra is called an A-algebra if all of its nilpotent subalgebras are abelian. These arise in the study of constant Yang-Mills potentials and have also been particularly important in relation to the problem of…
We investigate the class of finite dimensional not necessary associative algebras that have slowly growing length, that is, for any algebra in this class its length is less than or equal to its dimension. We show that this class is…
In one of our recent papers, the associative and the Lie algebras of Weyl type $A[D]=A\otimes F[D]$ were defined and studied, where $A$ is a commutative associative algebra with an identity element over a field $F$ of any characteristic,…
In this paper, we first present a classification theorem of infinite-dimensional simple Novikov algebras over an algebraically closed field with characteristic 0. Then we classify all the irreducible modules of a certain…
The class of associative trialgebras, also known as triassociative algebras, is characterized by three multiplications and eleven relations that generalize associativity. In the current paper, we present a study of nilpotent triassociative…
An infinite filiform Lie algebra L is residually nilpotent and its graded associated with respect to the lower central series has smallest possible dimension in each degree but is still infinite. This means that gr(L) is of dimension two in…