ABSTRACT
We give necessary conditions for the existence of degenerations between two complex Lie superalgebras of dimension . As an application, we study the variety
of complex Lie superalgebras of dimension
. First we give the algebraic classification and then obtain that
is the union of seven irreducible components, three of which are the Zariski closures of rigid Lie superalgebras. As a byproduct, we obtain an example of a nilpotent rigid Lie superalgebra, in contrast to the classical case where no example is known.
Acknowledgments
Both authors thank Ivan Kaygorodov for useful comments about the presentation of this paper.
Disclosure statement
No potential conflict of interest was reported by the authors.
ORCID
María Alejandra Alvarez http://orcid.org/0000-0002-2221-2325
Isabel Hernández http://orcid.org/0000-0002-4595-5228