|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'500'096
Articles rated: 2609
18 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Rankin-Cohen brackets and quantization of foliation, Part I: formal quantization | | Pierre Bieliavsky
; Xiang Tang
; Yijun Yao
; | | Date: |
24 Jun 2005 | | Subject: | Quantum Algebra MSC-class: 46L87; 58H05 | math.QA | | Abstract: | In this paper, we use the theory of deformation quantization to understand Connes’ and Moscovici’s results cite{cm:deformation}. We use Fedosov’s method of deformation quantization of symplectic manifolds to reconstruct Zagier’s deformation cite{z:deformation} of modular forms, and relate this deformation to the Weyl-Moyal product. We also show that the projective structure introduced by Connes and Moscovici is equivalent to the existence of certain geometric data in the case of foliation groupoids. Using the methods developed by the second author cite{t1:def-gpd}, we reconstruct a universal deformation formula of the Hopf algebra $calh_1$ associated to codimensional one foliations. In the end, we prove that the first Rankin-Cohen bracket $RC_1$ defines a noncommutative Poisson structure for an arbitrary $calh_1$ action. | | Source: | arXiv, math.QA/0506506 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser claudebot
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER