Some Twisted Results

Abstract

The Drinfeld twist for the opposite quasi-Hopf algebra is determined and is shown to be related to the (second) Drinfeld twist. The twisted Drinfeld twist is investigated. In the quasi-triangular case it is shown that the Drinfeld u operator arises from the equivalence of the opposite quasi-Hopf algebra to the quasi-Hopf algebra induced by twisting with the R-matrix. The Altschuler-Coste u operator arises in a similar way and is shown to be closely related to the Drinfeld u operator. The quasi-cocycle condition is introduced, and is shown to play a central role in the uniqueness of twisted structures on quasi-Hopf algebras. A generalisation of the dynamical quantum Yang-Baxter equation, called the quasi-dynamical quantum Yang-Baxter equation is introduced.

26 pages

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Cited by in corpus (2)

• Quantizations of generalized Cartan type $S$ Lie algebras and of the special algebra $\mathbf{S}(n;\underline{1})$ in the modular case
• Modular Quantizations of Lie Algebras of Cartan Type K via Drinfeld Twists of Jordanian Type