Poisson algebras associated to quasi-Hopf algebras

Abstract

We define admissible quasi-Hopf quantized universal enveloping (QHQUE) algebras by ℏ-adic valuation conditions. We show that any QHQUE algebra is twist-equivalent to an admissible one. We prove a related statement: any associator is twist-equivalent to a Lie associator. We attach a quantized formal series algebra to each admissible QHQUE algebra and study the resulting Poisson algebras.