Back to Search
Start Over
On Degenerations of Lie Superalgebras
- Publication Year :
- 2018
-
Abstract
- We give necessary conditions for the existence of degenerations between two complex Lie superalgebras of dimension $(m,n)$. As an application, we study the variety $\mathcal{LS}^{(2,2)}$ of complex Lie superalgebras of dimension $(2,2)$. First we give the algebraic classification and then obtain that $\mathcal{LS}^{(2,2)}$ is the union of seven irreducible components, three of which are the Zariski closures of rigid Lie superalgebras. As byproduct, we obtain an example of a nilpotent rigid Lie superalgebra, in contrast to the classical case where no example is known.<br />Comment: 12 pages
- Subjects :
- Mathematics - Rings and Algebras
17B30, 17B56, 17B99
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1802.08707
- Document Type :
- Working Paper