Quantization of coboundary Lie bialgebras

Details Quantization of coboundary Lie bialgebras Quantization of coboundary Lie bialgebras

2006-03-31

arxiv.org/abs/math/0603740v3

Ann. of Math. (2) 171 (2010), no. 2, 1267--1345

Mathematics

Quantum Algebra

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Scientific paper

We show that any coboundary Lie bialgebra can be quantized. For this, we prove that: (a) Etingof-Kazhdan quantization functors are compatible with Lie bialgebra twists, and (b) if such a quantization functor corresponds to an even associator, then it is also compatible with the operation of taking coopposites. We also use the relation between the Etingof-Kazhdan construction of quantization functors and the alternative approach to this problem, which was established in a previous work.

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