Timeline for Shuffle Hopf algebra: how to prove its properties in a slick way?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 4, 2011 at 20:03 | history | edited | DamienC | CC BY-SA 3.0 |
added 89 characters in body
|
| May 4, 2011 at 19:54 | comment | added | darij grinberg | Ah, that thing. Now I feel stupid for not remembering it from topology lectures :) | |
| May 4, 2011 at 19:52 | comment | added | DamienC | There is not that much analysis! The point is that iterated integrals are simply integrals over simplices (of products of pull-back of linear forms). Now if you want to express an integral over the cartesian product of two simplices in term of linear combinations of integrals over simplices, then you'll see that shuffles appear very naturally :-) | |
| May 4, 2011 at 19:43 | comment | added | darij grinberg | I will look into the loop integrals tomorrow. I need to be in good shape to understand analysis... | |
| May 4, 2011 at 19:43 | history | edited | DamienC | CC BY-SA 3.0 |
added 11 characters in body; deleted 4 characters in body
|
| May 4, 2011 at 19:42 | comment | added | darij grinberg | That recursive formula is actually my argument - one still must show that everything cancels out nicely. | |
| May 4, 2011 at 19:35 | history | edited | DamienC | CC BY-SA 3.0 |
reorganized paragraphs; deleted 12 characters in body
|
| May 4, 2011 at 19:31 | comment | added | DamienC | the formula for $S$ is equivalentto the following recursive one. For $x\in ker(\epsilon)$ one has $$ S(x)=-x-S(x')\star x'' $$ where $x'\otimes x''$ is the Sweedler notation for the reduced coproduct. Then you can prove by induction that it gives your easier formula. But I think that the loop interpretation is nicer (one does not need to compute a lot). | |
| May 4, 2011 at 19:21 | history | edited | DamienC | CC BY-SA 3.0 |
added 218 characters in body
|
| May 4, 2011 at 19:21 | comment | added | darij grinberg | It is not that clear to me how your formula for $S$ implies my part 2. But thanks for reminding me of the Manchon paper at a moment when I am actually near to a good printer! | |
| May 4, 2011 at 18:45 | history | edited | DamienC | CC BY-SA 3.0 |
added 53 characters in body; added 1 characters in body
|
| May 4, 2011 at 18:19 | history | edited | DamienC | CC BY-SA 3.0 |
added 1062 characters in body; added 2 characters in body
|
| May 4, 2011 at 17:55 | history | answered | DamienC | CC BY-SA 3.0 |