14 citations · 34 across the 8 of their papers we have counts for
8 papers
A classification of four-tuples of spinors of a ten dimensional space
Willem de Graaf, Alexander Elashvili, Mamuka Jibladze
We use the theory of theta-groups developed by Vinberg, along with computations in the computer algebra system GAP4, to classify the orbits of Spin(10,C)x SL(4,C) acting on the ten…
Semisimple cyclic elements in semisimple Lie algebras
A. G. Elashvili, M. Jibladze, V. G. Kac
This paper is a continuation of the theory of cyclic elements in semisimple Lie algebras, developed by Elashvili, Kac and Vinberg. Its main result is the classification of semisimp…
On Dynkin gradings in simple Lie algebras
A. G. Elashvili, M. Jibladze, V. G. Kac
In this paper we study gradings on simple Lie algebras arising from nilpotent elements. Specifically, we investigate abelian subalgebras which are degree 1 homogeneous with respect…
Cyclic elements in semisimple Lie algebras
A. G. Elashvili, V. G. Kac, E. B. Vinberg
A theory of cyclic elements in semisimple Lie algebras is developed. It is applied to an explicit construction of regular elements in Weyl groups.
Induced nilpotent orbits of the simple Lie algebras of exceptional type
W. A. de Graaf, A. G. Elashvili
We describe algorithms for computing the induced nilpotent orbits in semisimple Lie algebras. We use them to obtain the induction tables for the Lie algebras of exceptional type. T…
On exceptional nilpotents in semisimple Lie algebras
A. G. Elashvili, V. G. Kac, E. B. Vinberg
We classify all pairs (m,e), where m is a positive integer and e is a nilpotent element of a semisimple Lie algebra, which arise in the classification of simple rational W-algebras…