General form of the deformation of the Poisson superbracket on (2,n)-dimensional superspace

TL;DR

This paper characterizes all continuous formal deformations of the Poisson superbracket on certain superspaces, providing a comprehensive classification for cases where the Grassmann algebra has a number of generators not equal to two.

Contribution

It offers a complete description of the deformation space of the Poisson superbracket on (2,n)-dimensional superspaces for N ≠ 2, extending understanding of super-Poisson structures.

Findings

Classified all deformations up to equivalence for N ≠ 2

Identified the structure of deformations on superspaces with compact support functions

Extended previous results to a broader class of superspaces

Abstract

Continuous formal deformations of the Poisson superbracket defined on compactly supported smooth functions on R^2 taking values in a Grassmann algebra with N generating elements are described up to an equivalence transformation for N \ne 2.