Let $V$ be a vector space and $V^*$ the dual vector space. Let $T(V)$ be the tensor algebra of $V$. Is there some action $T(V^* \otimes V) \otimes T(V) \to T(V)$ and coaction $T(V) \to T(V^* \otimes V) \otimes T(V)$ such that $T(V)$ a Yetter-Drinfeld module over $T(V^* \otimes V)$? Thank you very much.
$\begingroup$
$\endgroup$
2
asked Jun 16, 2016 at 14:43
-
2$\begingroup$ Several of your recent questions have the form "is there some action such that" -- this seems like a bit of a fishing expedition to me. Why do you expect there to be such an action? How natural (functorial) do you want the action to be? Etc. $\endgroup$– Yemon ChoiCommented Jun 16, 2016 at 14:53
-
2$\begingroup$ Every vector space has at least some structure of Y-D module, the trivial one. In view of this, you probably want to be more precise about what you want. $\endgroup$– Mariano Suárez-ÁlvarezCommented Jun 16, 2016 at 19:08
Add a comment
|