Twisting of graded quantum groups and solutions to the quantum Yang-Baxter equation

Abstract: Let $H$ be a Hopf algebra over a field $k$ such that $H$ is $\mathbb Z$-graded as an algebra. In this talk, we introduce the notion of a twisting pair for $H$ and show that the Zhang twist of $H$ by such a pair can be realized as a 2-cocycle twist. We use twisting pairs to describe twists of Manin's universal quantum groups associated to quadratic algebras. Furthermore, we discuss a strategy to twist a solution to the quantum Yang-Baxter equation via the Faddeev-Reshetikhin-Takhtajan construction. If time permits, we illustrate this result for the quantized coordinate rings of $GL_n(k)$.

rings and algebrasrepresentation theory

Audience: researchers in the topic

ONCAS Online Noncommutative Algebra Seminar

Series comments: This is an online seminar organized to keep the community of noncommutative algebraists connected during the pandemic which has made it difficult for everyone to travel. If you would like to attend these talks, please email to any of the organizers and you will be added to the mailing list.