The moduli space of complex 5-dimensional Lie algebras

2015/10/01 by Alice Fialowski, Fialowski, Alice, Michael Penkava +1 · 1 citation
Mathematics · #13D10 #14B12 #14D15 #16E40 #16S80 #17B55 #17B70 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:13D10 #msc:14B12 #msc:14D15 #msc:16E40 #msc:16S80 #msc:17B55 #msc:17B70

paper · pdf · doi:10.48550/arxiv.1510.00285

arxiv created 2015/10/01 · arxiv updated 2015/10/02

Abstract

In this paper, we study the moduli space of all complex 5-dimensional Lie algebras, realizing it as a stratification by orbifolds, which are connected by jump deformations. The orbifolds are given by the action of finite groups on very simple complex manifolds. Our method of determining the stratification is based on the construction of versal deformations of the Lie algebras, which allow us to identify natural neighborhoods of the elements in the moduli space.

Cited by

• Deformations of the five dimensional Heisenberg Lie algebra

Related

• Moduli spaces of low dimensional Lie superalgebras
• The Moduli Space of Three Dimensional Lie Algebras
• The moduli space of 1|2-dimensional complex associative algebras
• The moduli space of 4-dimensional non-nilpotent complex associative algebras
• The moduli space of 2|1-dimensional complex associative algebras