Related papers: Primitive 4-generated axial algebras of Jordan typ…
Axial algebras are commutative nonassociative algebras generated by a finite set of primitive idempotents which action on an algebra is semisimple, and the fusion laws on the products between eigenvectors for these idempotents are…
We describe the variety of Jordan superalgebras of dimension $4$ whose even part is a Jordan algebra of dimension $2$ over an algebraically closed field $\mathbb{F}$ of characteristic $0$. We prove that the variety has $25$ irreducible…
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…
The purpose of this paper is a partial progress towards classification of simple infinite dimensional Jordan superalgebras. First, we prove that the only simple infinite dimensional Jordan superalgebras with finite dimensional even parts…
Decomposition algebras and axial decomposition algebras are classes of commutative nonassociative algebras which are generalizations of axial algebras. The classes decomposition algebras, axial decomposition al;gebras and non-primitive…
In this article, we first give a short introduction to conformal algebras. Then we present three families of simple conformal algebras finite growth generated by simple Jordan algebras of types A, B, C.
In the context of six-dimensional supergravity there is a special class of parent models for five-dimensional theories defined by the four Euclidean simple Jordan algebras of degree 3. We extend this result to include six- dimensional…
It is shown that the finite-dimensional simple representations of the super Jordan plane $B$ are one-dimensional. The indecomposable representations of dimension $2$ and $3$ of $B$ are classified. Two families of indecomposable…
In this paper we prove that $2$-generated primitive axial algebras of Monster type $(2\beta, \beta)$ over a ring $R$ in which $2$ and $\beta$ are invertible can be generated as $R$-module by $8$ vectors. We then completely classify…
This paper completes description of categories of representations of finite-dimensional simple unital Jordan superalgebras over algebraically closed field of characteristic zero.
We give a computional method to construct and classify nilpotent Jordan algebras over any arbitrary fields by the second cohomolgy of nilpotent Jordan algebras of low dimension "analogue of Skjelbred-Sund method", we see that every…
We construct Jordan algebras over a locally ringed space using generalizations of the Tits process and the first Tits construction by Achhammer. Some general results on the structure of these algebras are obtained. Examples of Albert…
The paper is devoted to the description of the varieties of complex 5-dimensional nilpotent Jordan superalgebras. We find all representatives for the isomorphism classes, using the Jordan normal form, results of simultaneous matrix…
We present a construction of a Jordan scheme from an elementary abelian $2$-group of rank $n$ and a $\{1,-1\}$-matrix of order $2^n$ that satisfies a specified condition. We then prove that the orders of matrices with the specified…
It is proved that the prime degenerate (-1,1) algebra constructed in [13] (the (-1,1)-monster) generates the same variety of algebras as the Grassman (-1,1)-algebra. Moreover, the same variety is generated by the Grassmann envelope of any…
Axial algebras are a class of non-associative commutative algebras whose properties are defined in terms of a fusion law. When this fusion law is graded, the algebra has a naturally associated group of automorphisms and thus axial algebras…
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…
We show that if $k$ is a countable field, then there exists a finitely generated, infinite-dimensional, primitive algebraic $k$-algebra $A$ whose Gelfand-Kirillov dimension is at most six. In addition to this we construct a two-generated…
We review various properties of the exceptional Euclidean Jordan algebra of degree three. Euclidean Jordan algebras of degree three and their corresponding Freudenthal triple systems were recently shown to be intimately related to extremal…
We study the general Jordan type of standard graded Artinian Gorenstein algebras, it is a finer invariant than Weak and Strong Lefschetz properties for those algebras. We prove that their Jordan types are determined by the rank of certain…