Hochschild cohomologies and deformations of the pointwise superproduct
Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 3, pp. 323-346 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the associative superalgebra of smooth compactly supported functions on $\mathbb R^n$ taking values in a Grassmann algebra. We find the lower Hochschild cohomologies and also the deformations of this superalgebra under certain additional conditions.
Mots-clés : deformation quantization
Keywords: quantum mechanics, superalgebra, Hochschild cohomology.
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S. E. Konstein; A. G. Smirnov; I. V. Tyutin. Hochschild cohomologies and deformations of the pointwise superproduct. Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 3, pp. 323-346. http://geodesic.mathdoc.fr/item/TMF_2009_158_3_a0/

[1] F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz, D. Sternheimer, Ann. Phys., 111:1 (1978), 61–110 ; 111–151 | DOI | MR | Zbl | DOI | MR | Zbl

[2] M. V. Karasev, V. P. Maslov, Nelineinye skobki Puassona. Geometriya i kvantovanie, Nauka, M., 1991 | MR | MR | Zbl

[3] B. Fedosov, Deformation Quantization and Index Theory, Math. Top., 9, Akademie, Berlin, 1996 | MR | Zbl

[4] M. Kontsevich, Lett. Math. Phys., 66:3 (2003), 157–216 ; arXiv: q-alg/9709040 | DOI | MR | Zbl

[5] N. A. Nekrasov, Trieste lectures on solitons in noncommutative gauge theories, arXiv: hep-th/0011095

[6] A. Schwarz, Gauge theories on noncommutative spaces, arXiv: hep-th/0011261

[7] H. J. Groenewold, Physica, 12:7 (1946), 405–460 | DOI | MR | Zbl

[8] F. A. Berezin, UFN, 132:3 (1980), 497–548 | DOI | MR

[9] I. V. Tyutin, TMF, 127:2 (2001), 253–267 ; arXiv: hep-th/0101046 | DOI | MR | Zbl

[10] D. A. Leites, I. M. Schepochkina, TMF, 126:3 (2001), 339–369 | DOI | MR | Zbl

[11] S. E. Konstein, I. V. Tyutin, General form of the deformation of Poisson superbracket on $(2,2)$-dimensional superspace, arXiv: hep-th/0612006

[12] J. Vey, Comment. Math. Helv., 50:1 (1975), 421–454 | DOI | MR | Zbl

[13] G. Pinczon, Lett. Math. Phys., 39:2 (1997), 143–156 | DOI | MR | Zbl

[14] V. V. Zharinov, TMF, 140:3 (2004), 355–366 | DOI | MR | Zbl

[15] S. E. Konshtein, A. G. Smirnov, I. V. Tyutin, TMF, 143:2 (2005), 163–194 ; arXiv: hep-th/0312109 | DOI | MR

[16] V. V. Zharinov, TMF, 136:2 (2003), 179–196 | DOI | MR | Zbl

[17] L. Khermander, Analiz lineinykh differentsialnykh operatorov s chastnymi proizvodnymi, T. 1, Mir, M., 1986 | MR | MR | Zbl