Semantic Scholar
Open Access
2004
11 sitasi
A simple algebraic proof of the algebraic index theorem
Po-Ning Chen
V. Dolgushev
Abstrak
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.
Topik & Kata Kunci
Penulis (2)
P
Po-Ning Chen
V
V. Dolgushev
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2004
- Bahasa
- en
- Total Sitasi
- 11×
- Sumber Database
- Semantic Scholar
- DOI
- 10.4310/MRL.2005.V12.N5.A4
- Akses
- Open Access ✓