Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Let $H$ be a Hopf algebra, $M$ a right $H$-comodule for a coaction $\Delta_R$, and $\triangleleft$ a right $H$-action on $M$ such that $M$ is a Yetter--Drindfeld module. We know from general theory that we have a corresponding braiding $$ \sigma: M \to M, ~~~~~~~~~~ m \otimes n \mapsto n_{(0)} \otimes (m \triangleleft n_{(1)}), $$ where $n_{(0)} \otimes n_{(1)}$ is the image of $n$ under $\Delta_R$.

Questions: (1) Can there exist another right action giving $M$ (still endowed with $\Delta_R$) the structure of a Yetter--Drinfeld module and producing the same braiding?

(2) Can there exist another right coaction giving $M$ (still endowed with $\triangleleft$) the structure of a Yetter--Drinfeld module and producing the same braiding?

(3) Do the answers to these questions change if $M$ is assumed to be finite dimensional?

share|improve this question
add comment

1 Answer

There are nonisomorpihic modules that have isomorphic $H$ and $H^*$ actions (and therefore isomorphic braidings?)

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.