Computation of the cohomology of a family of Z_2-graded Nilpotent Algebras

TL;DR

This paper computes the cohomology of specific Z_2-graded nilpotent algebras, extending known classifications in complex two-dimensional cases to more general finite-dimensional settings.

Contribution

It provides explicit cohomology calculations for a new class of nilpotent Z_2-graded algebras, generalizing previous low-dimensional results.

Findings

Explicit cohomology formulas derived for the algebras.

Identification of algebraic structures influencing cohomology.

Extension of known classifications to higher dimensions.

Abstract

In this paper we compute the cohomology of certain special cases of nilpotent algebras in a complex \zt-graded vector space of arbitrary finite dimension. These algebras are generalizations of the only two nontrivial complex 2-dimensional nilpotent algebras, one from the moduli space of $1|1$-dimensional algebras, and the other from the space of nongraded 2-dimensional algebras.