Vol. 291, No. 2, 2017

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A universal construction of universal deformation formulas, Drinfeld twists and their positivity

Chiara Esposito, Jonas Schnitzer and Stefan Waldmann

Vol. 291 (2017), No. 2, 319–358
Abstract

We provide an explicit construction of star products on U(g)-module algebras by using the Fedosov approach. This allows us to give a constructive proof to Drinfeld’s theorem and to obtain a concrete formula for Drinfeld twists. We prove that the equivalence classes of twists are in one-to-one correspondence with the second Chevalley–Eilenberg cohomology of the Lie algebra g. Finally, we show that for Lie algebras with Kähler structure we obtain a strongly positive universal deformation of -algebras by using a Wick-type deformation. This results in a positive Drinfeld twist.

Keywords
Star Product, Drinfeld twist, universal deformation formula
Mathematical Subject Classification 2010
Primary: 17B37
Secondary: 53D55, 81R50
Milestones
Received: 11 August 2016
Revised: 25 April 2017
Accepted: 9 May 2017
Published: 14 September 2017
Authors
Chiara Esposito
Institut für Mathematik, Lehrstuhl für Mathematik X
Universität Würzburg
D-97074 Würzburg
Germany
Jonas Schnitzer
Dipartimento di Matematica
Università degli Studi di Salerno
I-84084 Fisciano (SA)
Italy
Stefan Waldmann
Institut für Mathematik, Lehrstuhl für Mathematik X
Universität Würzburg
D-97074 Würzburg
Germany