Timeline for A weak Schur's lemma for non-semisimple finite dimensional algebras
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 14, 2019 at 22:39 | vote | accept | Sebastien Palcoux | ||
| Mar 14, 2019 at 20:35 | comment | added | Jeremy Rickard | @SebastienPalcoux For any finite dimensional algebra, there’s a bijection between (isomorphism classes of) indecomposable projective modules and simple modules, given by taking the quotient by the radical in one direction and taking the projective cover in the other. | |
| Mar 14, 2019 at 17:07 | comment | added | Sebastien Palcoux | Why the projective cover of a simple $kH$-module $S$ must be indecomposable and direct summand of $kH$? | |
| Mar 14, 2019 at 12:39 | comment | added | Jeremy Rickard | @SebastienPalcoux Not with group algebras, of course, as they'd be semisimple. But for abstract algebras I wouldn't expect the characteristic of $k$ to matter. It might just be harder to construct the examples because you don't have the groups to play with. | |
| Mar 14, 2019 at 12:25 | comment | added | Sebastien Palcoux | Do you expect the existence of a counter-example if the field is algebraically closed of characteristic zero? If yes, what about $k=\mathbb{C}$? | |
| Mar 14, 2019 at 9:15 | history | answered | Jeremy Rickard | CC BY-SA 4.0 |