Quantization of $r-Z$-quasi-Poisson manifolds and related modified classical dynamical $r$-matrices
| dc.creator | Halbout, Gilles | |
| dc.date | 2008-01-17 | |
| dc.date.accessioned | 2026-07-07T08:55:15Z | |
| dc.date.available | 2026-07-07T08:55:15Z | |
| dc.description | Le $X$ be a $C^\infty$-manifold and $\g$ be a finite dimensional Lie algebra acting freely on $X$. Let $r \in \ve^2(\g)$ be such that $Z=[r,r] \in \ve^3(\g)^\g$. In this paper we prove that every quasi-Poisson $(\g,Z)$-manifold can be quantized. This is a generalization of the existence of a twist quantization of coboundary Lie bialgebras (\cite{EH}) in the case $X=G$ (where $G$ is the simply connected Lie group corresponding to $\g$). We deduce our result from a generalized formality theorem. In the case Z=0, we get a new proof of the existence of (equivariant) formality theorem and so (equivariant) quantization of Poisson manifold ({\it cf.} \cite{Ko,Do}). As a consequence of our results, we get quantization of modified classical dynamical $r$-matrices over abelian bases in the reductive case | |
| dc.identifier | https://arxiv.org/abs/0801.2789 | |
| dc.identifier | http://arxiv.org/abs/0801.2789 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146214 | |
| dc.subject | Quantum Algebra | |
| dc.title | Quantization of $r-Z$-quasi-Poisson manifolds and related modified classical dynamical $r$-matrices | |
| dc.type | text |