| | |
| | |
Stat |
Members: 3643 Articles: 2'487'895 Articles rated: 2609
28 March 2024 |
|
| | | |
|
Article overview
| |
|
Kontsevich deformation quantization and flat connections | A. Alekseev
; C. Torossian
; | Date: |
1 Jun 2009 | Abstract: | In arXiv:math/0105152, the second author used the Kontsevich deformation
quantization technique to define a natural connection omega_n on the
compactified configuration spaces of n points on the upper half-plane. This
connection takes values in the Lie algebra of derivations of the free Lie
algebra with n generators. In this paper, we show that omega_n is flat.
The configuration space contains a boundary stratum at infinity which
coincides with the (compactified) configuration space of n points on the
complex plane. When restricted to this stratum, omega_n gives rise to a flat
connection omega_n^infty. We show that the parallel transport Phi defined by
omega_3^infty between configuration 1(23) and (12)3 verifies axioms of an
associator.
We conjecture that omega_n^infty takes values in the Lie algebra of
infinitesimal braids. This conjecture implies that Phi is an even Drinfeld
associator defining a new explicit solution of associator axioms. A proof of
this conjecture has recently appeared in arXiv:0905.1789 | Source: | arXiv, 0906.0187 | 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:
| |