Related papers: Semisimplifying Frank Lie algebras
Relying on the classification of simple Lie algebras over algebraically closed fields of characteristic $>3$, we show that any finite-dimensional central simple 5-graded Lie algebra over a field $k$ of characteristic $\neq 2,3$ is a simple…
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 considers the multiplicative Hom-Lie superalgebra structures on infinite dimensional simple Lie superalgebras of vector fields with characteristic zero. The main result is that there is only the multiplicative Hom-Lie…
Cardy-Frobenius algebra is the algebraic structure on the space of states in open-closed topological field theory. We prove that every semisimple super Cardy-Frobenius algebras is the direct sum of the super Cardy-Frobenius algebras of…
The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e. filiform Lie (super)algebras, into the theory of Lie algebras of order F$. Thus, the concept of filiform Lie algebras of order F is…
The adjoint action of a finite group of Lie type on its Lie algebra is studied. A simple formula is conjectured for the number of split semisimple orbits of a given genus. This conjecture is proved for type A, and partial results are…
We single out a large class of semisimple singularities with the property that all roots of the Poincar\'e polynomial of the Lie algebra of derivations of the corresponding suitably (not necessarily quasihomogeneously) graded moduli algebra…
In this expository article, we describe the classification of the subalgebras of the rank 2 semisimple Lie algebras. Their semisimple subalgebras are well-known, and in a recent series of papers, we completed the classification of the…
We define modular Terwilliger algebras of association schemes, Terwilliger algebras over a positive characteristic field, and consider basic properties. We give a condition for the modular Terwilliger algebra to be non-semisimple. We show…
The goal of this paper is to describe the structure of finite-dimensional semi-simple Leibniz algebras in characteristic zero. Our main tool in this endeavor are hemi-semidirect products. One of the major results of this paper is a…
We construct quasi-Hopf algebras associated with a semisimple Lie algebra, a complex curve and a rational differential. This generalizes our previous joint work with V. Rubtsov (Israel J. Math. (1999) and q-alg/9608005).
In this paper, we investigate semisimplicity of cellular algebras over positive characteristic fields. Our main result shows that the Frame number of cellular algebras characterizes semisimplicity of it. In a sense, this is a generalization…
We explicitly construct families of simple modules for Lie algebras of rank $2$, on which certain commutative subalgebra acts diagonally and has a simple spectrum. In type $A$ these modules are well known generic Gelfand-Tsetlin modules and…
This paper studies biderivations on finite-dimensional complex semisimple Lie algebras to their finite-dimensional modules. More precisely, we prove that all such symmetric biderivations are trivial. As applications, we determine all…
We study {\em disemisimple} Lie algebras, i.e., Lie algebras which can be written as a vector space sum of two semisimple subalgebras. We show that a Lie algebra $\mathfrak{g}$ is disemisimple if and only if its solvable radical coincides…
A new class of infinite dimensional simple Lie algebras over a field with characteristic 0 are constructed. These are examples of non-graded Lie algebras. The isomorphism classes of these Lie algebras are determined. The structure space of…
We describe a construction of an algebra over the field of order 2 starting from a conjugacy class of 3-transpositions in a group. In particular, we determine which simple Lie algebras arise by this construction. Among other things, this…
We study the semisimplicity of the category $KL_k$ for affine Lie superalgebras and provide a super analog of certain results from arXiv:1801.09880. Let $KL_k^{fin}$ be the subcategory of $KL_k$ consisting of ordinary modules on which the…
This paper is a further contribution to the extensive study by a number of authors of the subalgebra lattice of a Lie algebra. It is shown that, in certain circumstances, including for all solvable algebras, for all Lie algebras over…
Let $G$ be a finite group. There is a standard theorem on the classification of $G$-equivariant finite dimensional simple commutative, associative, and Lie algebras (i.e., simple algebras of these types in the category of representations of…