2021•arXiv (Cornell University)Open access

Can a Zhang twist be a cocycle twist

Hongdi Huang, Van C. Nguyen, Charlotte Ure, Kent B. Vashaw, Padmini Veerapen, Xingting Wang

Abstract

We provide sufficient conditions for a Zhang twist of a $\mathbb Z$-graded Hopf algebra $H$ to be again a Hopf algebra, to be an $H$-cleft object, or a 2-cocycle twist of $H$. In particular, we introduce the notion of a twisting pair for $H$ such that the Zhang twist of $H$ by such a pair is a 2-cocycle twist. This new notion is investigated in the context of various examples of Hopf algebras including Manin's universal quantum groups and quantized coordinate rings.

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Key concepts: Twist, Hopf algebra, Zhàng, Mathematics, Pure mathematics, Context (archaeology), Quantum group, Algebra over a field