Timeline for Bialgebras with rigid representation theory
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 25, 2021 at 8:02 | vote | accept | Jo Mo | ||
| Mar 22, 2021 at 18:06 | comment | added | Adrien | (I mean a unique one compatible with the duality of course). | |
| Mar 22, 2021 at 17:59 | comment | added | Adrien | In other words: for the fixed choice you made for a dual $V^*$ of some module $V$, there is a unique actual antipode on $B$ and a unique, canonical and natural isomorphism of $B$-module from your $V^*$ to the one induced by this antipode. It doesn't get better than that. | |
| Mar 22, 2021 at 17:58 | comment | added | Adrien | I'm not sure I understand your edit. Being rigid for a monoidal category is a property: either it is or it isn't, and then any two choices for a particular duality are canonically, naturally equivalent. So as you say even if you start with an Hopf algebra you can always cook up some choice of duality that is not equal to the standard one defined by the antipode, but those two choices are canonically isomorphic. (continued) | |
| Mar 22, 2021 at 17:46 | comment | added | Jo Mo | I have added a relevant edit to the question. | |
| Mar 22, 2021 at 17:35 | comment | added | Jo Mo | I am a bit confused. What do you mean by equivalent? My (second) question was whether $\alpha$ and $\beta$ are equal to 1 in the situation described above. In my situation, I wanted the rigid structure to be fixed and immutable. | |
| Mar 22, 2021 at 17:18 | history | answered | Adrien | CC BY-SA 4.0 |