Related papers: Superinvolutions on block-triangular matrix algebr…
We extend the Galilei group of space-time transformations by gradation, construct interacting field-theoretic representations of this algebra, and show that non-relativistic Super-Chern-Simons theory is a special case. We also study the…
We describe the ternary and the generalized superderivations of finite-dimensional semisimple Jordan superalgebras over an algebraically closed field of characteristic zero and of finite-dimensional simple Jordan superalgebras with…
Isomorphy classes of k-involutions have been studied for their correspondence with generalized symmetric spaces of algebraic groups. This is a continuation of papers written by A.G. Helminck and collaborators that are regarding algebraic…
We show that for fields that are of characteristic 0 or algebraically closed of characteristic greater than 5, that certain classes of Leibniz algebras are 2-recognizeable. These classes are solvable, strongly solvable and super solvable.…
Let $G=SL(2,5)$ be the special linear group of $2 \times 2$-matrices with coefficients in the field with $5$ elements. We show that the principal block over a splitting field $K$ of characteristic two of the group algebra $KG$ has a…
In the present paper we obtain the list of algebras, up to isomorphism, such that closure of any complex finite-dimensional algebra contains one of the algebra of the given list.
This article studies the set of R-equivalence classes of the group of proper projective similitudes of an algebra with involution of the first kind. The main results concern base fields of characteristic different from 2 over which every…
The algebra of embeddings at the I3 level has been deeply analyzed, but nothing is known algebra-wise for embeddings above I3. In this paper it is introduced an operation for embeddings at the level of I0 and above, and it is proven that…
The binomial interpolated transform of a sequence is a generalization of the well-known binomial transform. We examine a Pascal-like triangle, on which a binomial interpolated transform works between the left and right diagonals, focusing…
This paper is devoted to the study of Poisson superalgebras over fields of characteristic $2$. We investigate their representations, semidirect products, cohomology, formal deformations, and universal enveloping algebras. We also introduce…
An involution over finite fields is a permutation polynomial whose inverse is itself. Owing to this property, involutions over finite fields have been widely used in applications such as cryptography and coding theory. As far as we know,…
It is proved that for any finite dimensional representation of a prime order group over the field of rational numbers, polynomial invariants of degree at most $3$ separate the orbits. A result providing an upper degree bound for separating…
The article take up two-dimensional subalgebras from optimum system of algebra $L_{13}$, which is deduce from the gas dynamics equations. We calculated invariants and constructed invariant submodels for two-dimensional sabalgebras. Then…
The Drinfeld-Sokolov construction of integrable hierarchies, as well as its generalizations, may be extended to the case of loop superalgebras. A sufficient condition on the algebraic data for the resulting hierarchy to be invariant under…
Superderivations for the eight families of finite or infinite dimensional graded Lie superalgebras of Cartan-type over a field of characteristic $p>3$ are completely determined by a uniform approach: The infinite dimensional case is reduced…
In this paper, we classify Jordan superalgebras of dimension up to three over an algebraically closed field of characteristic different of two. Our main motivation to obtain such classification comes out from the intention to give an answer…
We study the geometry of super curves with a chosen supervolume form. We consider the algebra of divergence free vector fields $S(1|N)$ associated to such curves. When $N=2$ its derived algebra, called $S(2)$, defines a special family of…
We construct non-isogenous simple ordinary abelian varieties over an algebraic closure of a finite field with isomorphic endomorphism algebras.
Using the algebraic classification of all $2$-dimensional algebras, we give the algebraic classification of all $2$-dimensional rigid, conservative and terminal algebras over an algebraically closed field of characteristic 0. We have the…
We classify, up to isomorphism, all gradings by an arbitrary abelian group on simple finitary Lie algebras of linear transformations (special linear, orthogonal and symplectic) on infinite-dimensional vector spaces over an algebraically…