The quantum duality principle
Abstract
The "quantum duality principle" states that the quantization of a Lie bialgebra - via a quantum universal enveloping algebra (QUEA) - provides also a quantization of the dual Lie bialgebra (through its associated formal Poisson group) - via a quantum formal series Hopf algebra (QFSHA) - and, conversely, a QFSHA associated to a Lie bialgebra (via its associated formal Poisson group) yields a QUEA for the dual Lie bialgebra as well; more precisely, there exist functors QUEA --> QFSHA and QFSHA --> QUEA, inverse of each other, such that in either case the Lie bialgebra associated to the target object is the dual of that of the source object. Such a result was claimed true by Drinfeld, but seems to be unproved in literature: we give here a complete detailed proof of it.
Keywords
Cite
@article{arxiv.math/9909071,
title = {The quantum duality principle},
author = {Fabio Gavarini},
journal= {arXiv preprint arXiv:math/9909071},
year = {2017}
}
Comments
19 pages, AMS-TeX file. The paper has been entirely re-written: in particular, we add a discussion of the possible generalisation of the main result to the infinite dimensional case. This is the author's file of the final version (after the refereeing process), as sent for publication