Related papers: Ternary superderivations of Jordan superalgebras
We describe non-trivial $\delta$-derivations of semisimple finite-dimensional Jordan algebras over an algebraically closed field of characteristic not 2, and of simple finite-dimensional Jordan superalgebras over an algebraically closed…
We described $\delta$-derivations and $\delta$-superderivations of simple and semisimple finite-dimensional Jordan superalgebras over algebraic closed fields with characteristic $p\neq2$. We constructed new examples of 1/2-derivations and…
We introduce the concept of a $\delta$-superderivation of a superalgebra. $\delta$-Derivations of Cartan-type Lie superalgebras are treated, as well as $\delta$-superderivations of simple finite-dimensional Lie superalgebras and Jordan…
We classify decompositions of simple special finite-dimensional Jordan superalgebras over an algebraically closed field of characteristic zero into the sum of two proper simple subsuperalgebras.
This paper completes description of categories of representations of finite-dimensional simple unital Jordan superalgebras over algebraically closed field of characteristic zero.
We described $\delta$-derivations and $\delta$-superderivations of simple Jordan superalgebra <<KKM Double>> (also known as superalgebra of Jordan brackets) and unital simple finite-dimensional Jordan superalgebras over algebraic closed…
The maximal subalgebras of the finite dimensional simple special Jordan superalgebras over an algebraically closed field of characteristic 0 are studied. This is a continuation of a previous paper by the same authors about maximal…
In this paper, we give some construction about ternary Jordan algebras at first. Next we study relationships between generalized derivations, quasiderivations and centroids of ternary Jordan algebras. We show that for ternary Jordan…
In this paper, we mainly study the derivation algebras of semi-simple Jordan algebras over a field of characteristic $0$ and give sufficient and necessary conditions that the derivation algebras of them are simple. As an application, we…
I.P. Shestakov constructed an example of a unital simple special Jordan superalgebra over the field of real numbers. It turned out to be a subsuperalgebra of the Jordan superalgebra of vector type, but not isomorphic to a superalgebra of…
We classify simple finite Jordan conformal superalgebras and establish preliminary results for the classification of simple finite Jordan pseudoalgebras.
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…
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,…
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.
We classify all linearly compact simple Jordan superalgebras over an algebraically closed field of characteristic zero. As a corollary, we deduce the classification of all linearly compact unital simple generalized Poisson superalgebras.
We give the algebraic and geometric classification of complex four-dimensional Jordan superalgebras. In particular, we describe all irreducible components in the corresponding varieties.
In this paper, we mainly study Jordan derivations of dual extension algebras and those of generalized one-point extension algebras. It is shown that every Jordan derivation of dual extension algebras is a derivation. As applications, we…
We compare a number of different definitions of structure algebras and TKK constructions for Jordan (super)algebras appearing in the literature. We demonstrate that, for unital superalgebras, all the definitions of the structure algebra and…
We describe degenerations of three-dimensional Jordan superalgebras over $\mathbb{C}$. In particular, we describe all irreducible components in the corresponding varieties.
In this article we begin the study of representations of simple finite-dimensional noncommutative Jordan superalgebras. In the case of degree $\geq 3$ we show that any finite-dimensional representation is completely reducible and, depending…