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

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

2009-10-30

arxiv.org/abs/0910.5951v1

Mathematics

Rings and Algebras

20 pages

Scientific paper

In this paper, we study the moduli space of $1|2$-dimensional complex associative algebras, which is also the moduli space of codifferentials on the tensor coalgebra of a $2|1$-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.

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