The deformations of nondegenerate constant Poisson bracket with even and odd deformation parameters

TL;DR

This paper studies how nondegenerate constant Poisson superalgebras, defined on Grassmann-valued functions, can be deformed using both even and odd parameters, expanding understanding of their structural flexibility.

Contribution

It introduces explicit deformations of nondegenerate constant Poisson superalgebras with both even and odd parameters for the case n>1.

Findings

Deformations with even parameters are constructed.

Deformations with odd parameters are constructed.

Results apply to superalgebras on Grassmann-valued functions.

Abstract

We consider Poisson superalgebras with constant nondegenerate bracket realized on the smooth Grassmann-valued functions with compact supports in R^{2n}. The deformations with even and odd deformation parameters of these superalgebras are presented for n>1.