Cohomologies of the Poisson superalgebra

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

Cohomologies of the Poisson superalgebra

High Energy Physics - Theory 2007-05-23 v2

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

Abstract

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.

Keywords

Poisson superalgebra cohomology Grassmann-valued functions trivial representation adjoint representation Poisson superbracket

Cite

@article{arxiv.hep-th/0312109,
  title  = {Cohomologies of the Poisson superalgebra},
  author = {S. E. Konstein and A. G. Smirnov and I. V. Tyutin},
  journal= {arXiv preprint arXiv:hep-th/0312109},
  year   = {2007}
}

Comments

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

Cohomologies of the Poisson superalgebra

Abstract

Keywords

Cite

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