A Simple Algebraic Proof of the Algebraic Index Theorem

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dc.creatorChen, PoNing
dc.creatorDolgushev, Vasiliy
dc.date2004-08-16
dc.date2005-05-07
dc.date.accessioned2026-07-07T06:22:24Z
dc.date.available2026-07-07T06:22:24Z
dc.descriptionIn 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.
dc.description17 pages, no figures
dc.identifierhttps://arxiv.org/abs/math/0408210
dc.identifierhttp://arxiv.org/abs/math/0408210
dc.identifierMath. Res. Lett. Vol. 12, 5 (2005) 655-672.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/95901
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectK-Theory and Homology
dc.subject19A49; 19K56
dc.titleA Simple Algebraic Proof of the Algebraic Index Theorem
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