Timeline for Endomorphism Ring of Indecomposable MCM Modules
Current License: CC BY-SA 3.0
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| Oct 18, 2014 at 21:01 | comment | added | Floresza | It's not immediately clear Theorem 2.2 is applicable to the abelianization of the automorphism group, but a theorem of Leuschke shows that the Auslander Algebra has finite global dimension in the case of finite. Moreover, we are working in characteristic zero, so a theorem of Vaserstein applies (see the paper referenced in my original question). So, to summarize, understanding the endomorphism ring of these individual MCM modules allows us to understand something quite a bit bigger. Do you have a reference for these combinatorial methods? I would like to take a look. | |
| Oct 18, 2014 at 20:55 | comment | added | Floresza | Most of my education in the way of MCM modules has been through Yoshino's book. Another great (and slightly more modern) resource is Wiegand and Lueschke's book, "Cohen-Macaulay Representations". On a somewhat related note, it appears one might be able to compute the abelianization of the automorphism group without obtaining an explicit computation of the automorphism group or endomorphism ring (see Theorem 2.2 of this paper math.nju.edu.cn/~guoxj/articles/gp.pdf). | |
| Apr 9, 2014 at 19:09 | history | answered | Alex Dugas | CC BY-SA 3.0 |