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PDF and TeX files on arXiv, 2006, Lett.Math.Phys.79:109-129,2007,10.1007/s11005-006-0137-8, arXiv:math-ph/0507021v2

Abstract:

Authors' abstract presenting new results on quantization deformation on curves and Hochschild cohomology: "Deformation quantization on varieties with singularities offers perspectives that are not found on manifolds. The Harrison component of Hochschild cohomology, vanishing on smooth manifolds, reflects information about singularities. The Harrison 2--cochains are symmetric and are interpreted in terms of abelian products. This paper begins a study of abelian quantization on plane curves over C, being algebraic varieties of the form C2/R, where R is a polynomial in two variables; that is, abelian deformations of the coordinate algebra C[x,y]/(R). To understand the connection between the singularities of a variety and cohomologywe determine the algebraic Hochschild (co--)homology and its Barr--Gerstenhaber--Schack decomposition. Homology is the same for all plane curves C[x,y]/R, but the cohomology depends on the local algebra of the singularity of R at the origin. Keywords: Quantization, Deformation, Harrison Cohomology, Singular Curves Mathematics Subject Classifications (2000): 53D55, 14A22, 16E40, 16S60, 81S10 ."

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Open access: arXiv:math-ph/0507021v2 http://arxiv.org/PS_cache/math-ph/pdf/0507/0507021v2.pdf

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QuantizKonsevitch.pdf

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