Cohomologies of the Poisson superalgebra

Details Cohomologies of the Poisson superalgebra Cohomologies of the Poisson superalgebra

2003-12-10

arxiv.org/abs/hep-th/0312109v2

Theor.Math.Phys. 143 (2005) 625-650; Teor.Mat.Fiz. 143 (2005) 163-194

Physics

High Energy Physics

High Energy Physics - Theory

Comments: 40 pages, the text to appear in Theor. Math. Phys. supplemented by computation of the 3-rd trivial cohomology

Scientific paper

Cohomology spaces of the Poisson superalgebra realized on smooth Grassmann-valued functions with compact support on $R^{2n}$ ($C^{2n}) are investigated under suitable continuity restrictions on cochains. The first and second cohomology spaces in the trivial representation and the zeroth and first cohomology spaces in the adjoint representation of the Poisson superalgebra are found for the case of a constant nondegenerate Poisson superbracket for arbitrary n>0. The third cohomology space in the trivial representation and the second cohomology space in the adjoint representation of this superalgebra are found for arbitrary n>1.

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