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Deformations of the antibracket with Grassmann-valued deformation parameters

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Abstract

We consider the antibracket superalgebra realized on the space of smooth functions on ℝ1 with values in the Grassmann algebra with one generator ξ and consisting of elements of the form ξf 0 (x) + f 1 (x) with compactly supported f 0 . Any basis of the second cohomology space with coefficients in the adjoint representation of this superalgebra consists of three odd and infinitely many even elements. We describe a large class of deformations of this superalgebra with Grassmann-valued deformation parameters. In particular, we find all deformations of this superalgebra that have exactly three odd parameters.

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Authors and Affiliations

  1. Tamm Department of Theoretical Physics, Lebedev Physical Institute, RAS, Moscow, Russia

    S. E. Konstein & I. V. Tyutin

  2. Scientific Research Institute of Experimental and Theoretical Physics, Al-Farabi Kazakh National University, Almaty, Kazakhstan

    S. E. Konstein

  3. Tomsk State Pedagogical University, Tomsk, Russia

    I. V. Tyutin

Authors
  1. S. E. Konstein
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  2. I. V. Tyutin
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Correspondence to S. E. Konstein.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 183, No. 1, pp. 62–77, April, 2015.

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Konstein, S.E., Tyutin, I.V. Deformations of the antibracket with Grassmann-valued deformation parameters. Theor Math Phys 183, 501–515 (2015). https://doi.org/10.1007/s11232-015-0277-z

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  • DOI: https://doi.org/10.1007/s11232-015-0277-z

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