| Reference : An explicit two step quantization of Poisson structures and Lie bialgebras |
| Scientific journals : Article | |||
| Physical, chemical, mathematical & earth Sciences : Mathematics | |||
| http://hdl.handle.net/10993/28968 | |||
| An explicit two step quantization of Poisson structures and Lie bialgebras | |
| English | |
Merkulov, Sergei  [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] | |
| Willwacher, Thomas [ETH, Zurich > Mathematics] | |
| 2018 | |
| Communications in Mathematical Physics | |
| Springer | |
| 364 | |
| 2 | |
| 505–578 | |
| Yes (verified by ORBilu) | |
| 0010-3616 | |
| 1432-0916 | |
| Germany | |
| [en] Quantization ; Poisson structures ; Lie bialgebras | |
| [en] We develop a new approach to deformation quantizations of Lie bialgebras and Poisson structures which goes in two steps.
In the first step one associates to any Poisson (resp. Lie bialgebra) structure a so called quantizable Poisson (resp. Lie bialgebra) structure. We show explicit transcendental formulae for this correspondence. In the second step one deformation quantizes a quantizable Poisson (resp. Lie bialgebra) structure. We show again explicit transcendental formulae for this second step correspondence (as a byproduct we obtain configuration space models for biassociahedron and bipermutohedron). In the Poisson case the first step is the most non-trivial one and requires a choice of an associator while the second step quantization is essentially unique, it is independent of a choice of an associator and can be done by a trivial induction. We conjecture that similar statements hold true in the case of Lie bialgebras. The main new result is a surprisingly simple explicit universal formula (which uses only smooth differential forms) for universal quantizations of finite-dimensional Lie bialgebras. | |
| http://hdl.handle.net/10993/28968 | |
| 57 pages |
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