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Teoreticheskaya i Matematicheskaya Fizika, 2015, Volume 183, Number 1, Pages 62–77
DOI: https://doi.org/10.4213/tmf8794 (Mi tmf8794) 		 
Deformations of the antibracket with Grassmann-valued deformation parameters

S. E. Konsteinab, I. V. Tyutinac

a Tamm Department of Theoretical Physics, Lebedev Physical Institute, RAS, Moscow, Russia
b Scientific Research Institute of Experimental and Theoretical Physics, Al-Farabi Kazakh National University, Almaty, Kazakhstan.
c Tomsk State Pedagogical University, Tomsk, Russia
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DOI: https://doi.org/10.4213/tmf8794
Abstract: We consider the antibracket superalgebra realized on the space of smooth functions on $\mathbb{R}^1$ with values in the Grassmann algebra with one generator $\xi$ and consisting of elements of the form $\xi f_0(x)+f_1(x)$ 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.
Keywords: antibracket, deformation, cohomology, Poisson superalgebra.
Funding agency Grant number
Russian Foundation for Basic Research 14-02-01171
14-01-00489
Received: 15.09.2014
English version:
Theoretical and Mathematical Physics, 2015, Volume 183, Issue 1, Pages 501–515
DOI: https://doi.org/10.1007/s11232-015-0277-z
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. E. Konstein, I. V. Tyutin, “Deformations of the antibracket with Grassmann-valued deformation parameters”, TMF, 183:1 (2015), 62–77; Theoret. and Math. Phys., 183:1 (2015), 501–515
Citation in format AMSBIB
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