The moduli space of 2|1-dimensional complex associative algebras

2009/10/23 by Chris DeCleene, Carolyn Otto, DeCleene, Chris +9
Mathematics · #13D10 #14B12 #14D15 #16E40 #16S80 #17B55 #17B70 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #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.0910.4430

24 pages

arxiv created 2009/10/23 · openalex publication_date 2009/10/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the moduli space of 2|1-dimensional complex associative algebras, which is also the moduli space of codifferentials on the tensor coalgebra of a 1|2-dimensional complex space. We construct the moduli space by considering extensions of lower dimensional algebras. We also construct miniversal deformations of these algebras. This gives a complete description of how the moduli space is glued together via jump deformations.

Citations

• Extensions of associative algebras

Related

• The moduli space of 1|2-dimensional complex associative algebras
• The moduli space of 1|1-dimensional complex associative algebras
• The moduli space of complex two dimensional associative algebras
• The moduli space of 4-dimensional non-nilpotent complex associative algebras
• The moduli space of 3-dimensional associative algebras