THE LOCAL INDEX FORMULA IN NONCOMMUTATIVE GEOMETRY
THE LOCAL INDEX FORMULA IN NONCOMMUTATIVE GEOMETRY
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DOI：
10.1007/bf01895667
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发表时间：
1995-01-01
影响因子：
2.2
通讯作者：
MOSCOVICI, H
中科院分区：
文献类型：
--
作者：
CONNES, A;MOSCOVICI, H
在非交换几何中，几何空间从谱Vantage被描述为一个三元组（A，H，D），由一个在希尔伯特空间H中表示的 *-代数A和一个无界自伴算子D组成，算子D具有紧预解式，它以有界的方式与代数相互作用。本文在两个重要方面推进了这一观点：（1）通过证明流形的任何变换的伪群产生这样一个有限可和度的谱三元组，（2）通过证明一个一般的，在某种意义上通用的，有限可和度的任意谱三元组的局部指标公式，根据Dixloun迹及其剩余型扩张。
In noncommutative geometry a geometric space is described from a spectral vantage point, as a triple (A, H, D) consisting of a *-algebra A represented in a Hilbert space H together with an unbounded selfadjoint operator D, with compact resolvent, which interacts with the algebra in a bounded fashion. This paper contributes to the advancement of this point of view in two significant ways: (1) by showing that any pseudogroup of transformations of a manifold gives rise to such a spectral triple of finite summability degree, and (2) by proving a general, in some sense universal, local index formula for arbitrary spectral triples of finite summability degree, in terms of the Dixmier trace and its residue-type extension.