Some irreducible components of the variety of complex (n+1)-dimensional Leibniz algebras

Abstract

In the present paper we indicate some Leibniz algebras whose closures of orbits under the natural action of GLn form an irreducible component of the variety of complex n-dimensional Leibniz algebras. Moreover, for these algebras we calculate the bases of their second groups of cohomologies.

New examples of infinite-dimensional n-Lie algebras

“…It is known that a Lie algebra with vanishing adjoint cohomology is rigid and the closure of its orbit determines the irreducible components of the variety [13]. This is a motivation of many works focused to discovering algebras with open orbits and to describe sufficient properties of such algebras [1,6,11,15,16].…”