#### 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 $\mathsc{U}\left(\mathfrak{g}\right)$-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 $\mathfrak{g}$. Finally, we show that for Lie algebras with Kähler structure we obtain a strongly positive universal deformation of ${}^{\ast }$-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