Timeline for The Jacobson radical of an infinite dimensional algebra
Current License: CC BY-SA 3.0
5 events
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| Nov 12, 2011 at 3:54 | vote | accept | Yaping Yang | ||
| Sep 2, 2011 at 7:58 | history | edited | Torsten Ekedahl | CC BY-SA 3.0 |
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| Sep 2, 2011 at 6:56 | comment | added | Julian Kuelshammer | You are right. The situation is more similar to the polynomial ring in one variable. What you do is conceptually reducing the algebra $A$ to $e_1Ae_1$, where $e_1$ is the trivial path for one point. $e_1Ae_1$ is then the polynomial ring in one variable, which has only finite dimensional representations. By general theory the functor $F: A-mod\to e_1Ae_1-mod, M\mapsto e_1 M$ sends irreducibles to irreducibles (or zero, which can be excluded in our case). Your argument then shows that irreducible modules are finite dimensional for the polynomial ring. | |
| Sep 2, 2011 at 6:15 | history | edited | Torsten Ekedahl | CC BY-SA 3.0 |
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| Sep 2, 2011 at 5:49 | history | answered | Torsten Ekedahl | CC BY-SA 3.0 |