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Higher localized analytic indices and strict deformation quantization.

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Title: Higher localized analytic indices and strict deformation quantization.
Authors: Rouse, Paulo Carrillo
Source: Deformation Spaces; 2010, p91-111, 21p
Abstract: This paper is concerned with the localization of higher analytic indices for Lie groupoids. Let G be a Lie groupoid with Lie algebroid AG. Let τ be a (periodic) cyclic cocycle over the convolution algebra ]> We say that τ can be localized if there is a morphism ]> satisfying Indτ (a)=〈ind Da, τ ❭ (Connes pairing). In this case, we call Indτ the higher localized index associated to τ. In [CR08a] we use the algebra of functions over the tangent groupoid introduced in [CR08b], which is in fact a strict deformation quantization of the Schwartz algebra S(AG ), to prove the following results: Every bounded continuous cyclic cocycle can be localized. If G is étale, every cyclic cocycle can be localized. We will recall this results with the difference that in this paper, a formula for higher localized indices will be given in terms of an asymptotic limit of a pairing at the level of the deformation algebra mentioned above. We will discuss how the higher index formulas of Connes-Moscovici, Gorokhovsky-Lott fit in this unifying setting. [ABSTRACT FROM AUTHOR]
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DOI: 10.1007/978-3-8348-9680-3_4
Database: Complementary Index
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