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Algebraic index theorem. (English) Zbl 0887.58050

This paper is the first in a series aimed at providing an algebraic insight to various Atiyah-Singer type index theorems: We prove the Atiyah-Singer index theorem where the algebra of pseudo-differential operators is replaced by an arbitrary deformation quantization of the algebra of functions on a symplectic manifold.

MSC:

58J20 Index theory and related fixed-point theorems on manifolds
53D55 Deformation quantization, star products
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