Timeline for Whether Morita equivalence holds the following properties?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 22, 2016 at 13:28 | comment | added | Mare | it can be found in the book of skowronski and yamgata "frobenius algebras I" somewhere I think. It is also not hard to see it via Morita theory. | |
| Oct 22, 2016 at 13:26 | comment | added | Xiaosong Peng | @Mare Hello, sir. I don't know this result " two algebras over an algebraically closed field are Morita equivalent iff their quiver algebras are isomorphic", could you tell me where to find it? | |
| Oct 22, 2016 at 13:22 | vote | accept | Xiaosong Peng | ||
| Oct 22, 2016 at 13:18 | comment | added | Mare | no, but to get the necessary information you just need a resolution of a module which contains every indecomposable projective module (and just such modules) as a direct summand and this is the case. | |
| Oct 22, 2016 at 13:16 | comment | added | Xiaosong Peng | @Mare For question 2), I know that Morita equivalence holds these properties. But given a minimal injective resolution of $A$, can you make sure the equivalence maps $A$ to $B$? | |
| Oct 22, 2016 at 13:13 | comment | added | Mare | It is not really easy, I should have said "easy, compared to check derived equivalence". | |
| Oct 22, 2016 at 13:12 | comment | added | Benjamin Steinberg | How easy is it really to compute a quiver presentation from say structure constants for the algebra? There are very few monoid algebras for which I know how to do it. | |
| Oct 22, 2016 at 13:09 | history | answered | Mare | CC BY-SA 3.0 |