Timeline for Is the homotopy category of a ring also the derived category of another ring?
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| Jul 6, 2014 at 19:42 | comment | added | Jeremy Rickard | If $R$ is an artinian ring of finite representation type (and I think it's still an open question whether this is equivalent to being pure semisimple?) then I think $K(R)$ is equivalent to $D(S)$ for $S$ the Auslander algebra of $R$ (i.e., the endomorphism ring of the direct sum of all indecomposable modules, or its opposite ring, depending on your choice of conventions). I'm confident of this if $R$ is an artin algebra (i.e., finitely generated as a module over an artinian centre), but I might be missing a problem for general artinian rings. | |
| Jul 6, 2014 at 18:19 | history | answered | Greg Stevenson | CC BY-SA 3.0 |