экспонента многообразия

New Properties of Almost Nilpotent Variety of Exponent 2

Authors: Shulezhko O. V.

In the presented work we consider numerical characteristics of almost nilpotent variety of exponent 2, which was first constructing in article [1]. The main result of this paper is introduce the exact values of the multiplicities of the irreducible modules appearing in the expansion of the multilinear part of the variety. Meanwhile, we obtain as a consequence the formulas of codimension and colength of the variety of exponent 2.

On Subvariety of Variety Generated by a Simple Infinite Lie Algebra of Cartan Type General Series W2

Authors: Bogdanchuk O. A.
We consider numerical characteristics of Lie algebras variety over a field of characteristic zero, basically, the exponent of variety.
Here, was constructed the infinite series of varieties of Lie algebras with different fractional exponents, which belong to variety
generated by a simple infinite Lie algebra of Cartan type general series W2.