S. E. Konstein, A. G. Smirnov, I. V. Tyutin, “General form of the deformation of the Poisson superbracket”, TMF, 2006, Volume 148, Number 2,Pages <nobr>163

This article is cited in 5 papers

General form of the deformation of the Poisson superbracket

S. E. Konstein, A. G. Smirnov, I. V. Tyutin

P. N. Lebedev Physical Institute, Russian Academy of Sciences

Abstract: All continuous formal deformations of the Poisson algebra realized on Grassmann-valued compactly supported smooth functions on $\mathbb R^{2n}$ with $2n\ge4$ are found up to an equivalence transformation. We show that in the algebras considered, there exist additional deformations that differ from the Moyal bracket.

Keywords: Grassmann algebra, Poisson superalgebra, central extension, cohomologies, $*$-commutator, deformation, quantization.

Received: 12.12.2005

DOI: 10.4213/tmf2078