Timeline for What is the comultiplication of a matrix frobenius algebra?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 1, 2009 at 10:45 | comment | added | Aleks Kissinger | That's the point! In fact, this type of frobenius algebra (called special FA) uniquely picks out a basis in the underlying object. We often take this as a pure categorical way to define basis. See eg Coecke et al's "Bases" paper. | |
| Oct 31, 2009 at 23:37 | comment | added | Theo Johnson-Freyd | Incidentally, your proscription for defining a frobenius algebra on a finite-dimensional vector space requires a basis. Otherwise your comultiplication and counit are not linear. | |
| Oct 29, 2009 at 12:19 | comment | added | Aleks Kissinger | Maybe this is all there really is to say about this co-multiply. I was just wondering if there's something else there, like this example: Define a frobenius algebra on any FD vector space by making comultiply "copy" a basis. delta :: |i> |-> |ii> and counit "delete" a basis. epsilon :: |i> |-> 1. Mult. and unit are just the daggers. For delta_X defined on the eigenvectors of Pauli X (|+>, |->), it's a (happily coincidental?) fact that the induced multiply delta^dag is actually logical XOR on the Pauli Z basis (|0>, |1>). | |
| Oct 27, 2009 at 20:59 | answer | added | Theo Johnson-Freyd | timeline score: 8 | |
| Oct 27, 2009 at 16:51 | history | edited | Kim Morrison | CC BY-SA 2.5 |
added 5 characters in body; edited title
|
| Oct 27, 2009 at 12:21 | comment | added | Simon Wadsley | I don't quite see why you aren't happy with the intuition that you give. It seems to me that it cleanly describes what the comultiplication is and how it arises. | |
| Oct 27, 2009 at 11:41 | history | asked | Aleks Kissinger | CC BY-SA 2.5 |