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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 R1 with values in the Grassmann algebra with one generator ξ and consisting of elements of the form ξf0(x)+f1(x) with compactly supported f0. 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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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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