S. E. Konstein, A. G. Smirnov, I. V. Tyutin, “Hochschild cohomologies and deformations of the pointwise superproduct”, TMF, 2009, Volume 158, Number 3,Pages <nobr>323

Hochschild cohomologies and deformations of the pointwise superproduct

S. E. Konstein^a, A. G. Smirnov^a, I. V. Tyutin^ab

^a P. N. Lebedev Physical Institute, Russian Academy of Sciences
^b Universidade de São Paulo

Abstract: 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.

Keywords: deformation quantization, quantum mechanics, superalgebra, Hochschild cohomology.

Received: 24.06.2009

DOI: 10.4213/tmf6317