A Universal Construction of Universal Deformation Formulas, Drinfel'd Twists and their Positivity
Abstract
In this paper we provide an explicit construction of star products on U(g)-module algebras by using the Fedosov approach. This construction allows us to give a constructive proof to Drinfel'd theorem and to obtain a concrete formula for Drinfel'd twist. 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 Drinfel'd twist.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2016
- DOI:
- 10.48550/arXiv.1608.00412
- arXiv:
- arXiv:1608.00412
- Bibcode:
- 2016arXiv160800412E
- Keywords:
-
- Mathematics - Quantum Algebra
- E-Print:
- 31 pages, added Remark 5.8