A Simple Algebraic Proof of the Algebraic Index Theorem
Quantum Algebra
2007-05-23 v3 High Energy Physics - Theory
K-Theory and Homology
Abstract
In math.QA/0311303 B. Feigin, G. Felder, and B. Shoikhet proposed an explicit formula for the trace density map from the quantum algebra of functions on an arbitrary symplectic manifold M to the top degree cohomology of M. They also evaluated this map on the trivial element of K-theory of the algebra of quantum functions. In our paper we evaluate the map on an arbitrary element of K-theory, and show that the result is expressed in terms of the A-genus of M, the Deligne-Fedosov class of the quantum algebra, and the Chern character of the principal symbol of the element. For a smooth (real) symplectic manifold (without a boundary), this result implies the Fedosov-Nest-Tsygan algebraic index theorem.
Cite
@article{arxiv.math/0408210,
title = {A Simple Algebraic Proof of the Algebraic Index Theorem},
author = {PoNing Chen and Vasiliy Dolgushev},
journal= {arXiv preprint arXiv:math/0408210},
year = {2007}
}
Comments
17 pages, no figures