Related papers: The Kac Jordan superalgebra: automorphisms and max…
The group-scheme of automorphisms of the ten-dimensional exceptional Kac's Jordan superalgebra is shown to be isomorphic to the semidirect product of the direct product of two copies of SL2 by the constant group scheme C2. This is used to…
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…
Models of all the gradings on the exceptional simple Lie algebras induced by Jordan subgroups of their groups of automorphisms are provided.
The groups of automorphisms of the Jacobian algebras are found.
We classify abelian subgroups of the automorphism group of any compact simple Lie algebra whose centralizer has the same dimension as the dimension of the subgroup. This leads to a classification of the maximal abelian subgroups of compact…
Kac's ten-dimensional simple Jordan superalgebra over a field of characteristic 5 is obtained from a process of semisimplification, via tensor categories, from the exceptional simple Jordan algebra (or Albert algebra), together with a…
We give the algebraic and geometric classification of complex four-dimensional Jordan superalgebras. In particular, we describe all irreducible components in the corresponding varieties.
The automorphisms groups and derivation algebras of all two-dimensional algebras over algebraically closed fields are described.
With this paper we start a programme aiming at connecting two vast scientific areas: Jordan algebras and representation theory. Within representation theory, we focus on non-compact, real forms of semisimple Lie algebras and groups as well…
We classify simple finite Jordan conformal superalgebras and establish preliminary results for the classification of simple finite Jordan pseudoalgebras.
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.
We classify the gradings on the Kac superalgebra up to equivalence.
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.
In this paper we describe all subalgebras and automorphisms of simple noncommutative Jordan superalgebras $K_3(\alpha,\beta,\gamma)$ and $D_t(\alpha,\beta,\gamma)$ and compute the derivations of the nontrivial simple finite-dimensional…
A Kac-Moody algebra is called hyperbolic if it corresponds to a generalized Cartan matrix of hyperbolic type. We study root subsystems of root systems of hyperbolic algebras. In this paper, we classify maximal rank regular hyperbolic…
We describe the structure of the algebraic group of automorphisms of all simple finite dimensional Lie superalgebras. Using this and \'etale cohomology considerations, we list all different isomorphism classes of the corresponding twisted…
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 classify closed abelian subgroups of the automorphism group of any compact classical simple Lie algebra whose centralizer has the same dimension as the dimension of the subgroup, and describe Weyl groups of maximal abelian subgroups.
A complete classifications of two-dimensional general, commutative, commutative Jordan, division and evolution real algebras are given. In the case of evolution algebras their groups of automorphisms and derivation algebras are described as…
We compute the graded automorphisms of the upper triangular matrices, viewed as associative, Lie and Jordan algebras. We compute also the so called self-equivalences and Weyl and diagonal groups for every grading.