S. E. Konstein, I. V. Tyutin, “General form of the deformation of the Poisson superbracket on a <nobr>$(2,n)$</nobr>-dimensional superspace”, TMF, 2008, Volume 155, Number 2,Pages <nobr>265

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

S. E. Konstein, I. V. Tyutin

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

Abstract: Up to an equivalence transformation, we describe continuous formal deformations of the Poisson superbracket defined on compactly supported smooth functions on $\mathbb R^2$ taking values in a Grassmann algebra $\mathbb G^{n_-}$.

Keywords: cohomology of Lie algebras, deformation of Lie algebras, Poisson superbracket, quantization.

Received: 04.04.2007

DOI: 10.4213/tmf6210