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.
A universal construction of universal deformation formulas, Drinfeld twists and their positivity
Esposito, ChiaraMembro del Collaboration Group
;SCHNITZER, JONAS CHRISTOPH;
2017
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.File in questo prodotto:
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