Timeline for an inverse semigroup (and perhaps a $C^*\!$-algebra) associated with a directed graph
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 11, 2018 at 19:54 | vote | accept | David Hillman | ||
| Mar 26, 2018 at 19:52 | comment | added | Benjamin Steinberg | I got rid of them because they were mostly about the standard graph C*-algebra. Basically you should not need to put the additive relations into your semigroup. They come for free when you use Exel's tight algebra construction. This comes by taking the universal groupoid of the inverse semigroup and reducing to the closure of the ultrafilters. This will automatically impose you relations 3. | |
| Mar 26, 2018 at 18:41 | comment | added | David Hillman | Hey, Benjamin, where did your first two comments go? About the universal $C^*\!$-algebra, etc? They were interesting! Did I make them go away somehow?? :-( | |
| Mar 26, 2018 at 18:03 | comment | added | David Hillman | A weird thing about this is: the above construction is very useful for understanding flow equivalence maps of SFTs from an algebraic point of view. And yet, the $C^*\!$-algebras that have been used to obtain flow equivalence invariants are, as far as I know, the graph $C^*\!$-algebras, which, as you mentioned, are different! | |
| Mar 26, 2018 at 17:57 | comment | added | David Hillman | I take it you mean length-0 paths? Yes: these correspond to the quantities given in (3): you could call that idempotent $1_v$, the length-0 path beginning and ending at $v$. | |
| Mar 26, 2018 at 17:52 | comment | added | David Hillman | (Note: I just edited my question to add that last paragraph about partially defined multiplication.) The sum of zero items is taken to be zero (in answer to your question about sources and sinks). | |
| Mar 26, 2018 at 17:50 | comment | added | Benjamin Steinberg | Do you allow empty paths? | |
| Mar 26, 2018 at 17:46 | history | edited | David Hillman | CC BY-SA 3.0 |
added 342 characters in body
|
| Mar 26, 2018 at 17:09 | comment | added | Benjamin Steinberg | How do you want to interpret (3) if there are sources or sinks? | |
| Mar 26, 2018 at 16:59 | answer | added | Benjamin Steinberg | timeline score: 1 | |
| Mar 26, 2018 at 15:22 | history | edited | David Hillman | CC BY-SA 3.0 |
added 31 characters in body
|
| Mar 26, 2018 at 15:08 | history | asked | David Hillman | CC BY-SA 3.0 |