Cluster tilting and complexity
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Thu, 15/10/2009 14:30 |
Petter Bergh (NTNU Trondheim) |
Representation Theory Seminar  |
L3 |
| This is joint work with Steffen Oppermann. A cluster category is obtained from the bounded derived category of a hereditary algebra, by forming the orbit category with respect to the suspension and the Auslander-Reiten translate. We study the complexity between objects in this triangulated category, and show the following: the maximal complexity occurring is either one, two or infinite, depending on whether the original algebra is of finte, tame or wild representation type. Moreover, we show that the complexity of a module over a tame cluster tilted algebra is at most one. | |||