Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher localized analytic indices and strict deformation quantization   This paper is concerned with the localization of higher analytic indices for
Lie groupoids. Let $\gr$ be a Lie groupoid with Lie algebroid $A\gr$. Let
$\tau$ be a (periodic) cyclic cocycle over the convolution algebra $\cg$. We
say that $\tau$ can be localized if there is a correspondence
K^0(A^*\gr)\stackrel{Ind_{\tau}}{\longrightarrow}\mathbb{C} satisfying
$Ind_{\tau}(a)=< ind D_a,\tau>$ (Connes pairing). In this case, we call
$Ind_{\tau}$ the higher localized index associated to $\tau$. In {Ca4} we use
the algebra of functions over the tangent groupoid introduced in {Ca2}, which
is in fact a strict deformation quantization of the Schwartz algebra
$\sw(A\gr)$, to prove the following results: \item Every bounded continuous
cyclic cocycle can be localized. \item If $\gr$ is {\'e}tale, 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.

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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat