Lutz Hille (Uni Münster): On the number of tilting modules for Dynkin quivers
via polytopes (Oberseminar Algebra und Geometrie)
Wednesday, 09.04.2014 16:30 im Raum N 2
The number of tilting modules is classical known for type A and type D
and recently attracted attention again in the work of Ringel and his
coauthors. Moreover, certain closely related numbers also have been
considered: the number of rigid modules, the number of exceptional
sequences, the number of cluster tilting modules and the number of
tilting complexes.
The aim of this talk is to relate all these numbers and to unify the
computation, so that it is not case by case anymore. Moreover, the
number of tilting modules does not depend on the orientation, however,
so far, the computation depends on a choice of the orientation of the
quiver. The principal idea is to define certain polytopes, so that the
volume of these polytopes coincides with the number of tilting modules.
Using this approach, we obtain several recursion formulas that relate
the these numbers and allow to compute them in one strike for all Dynkin
quivers and all orientations.
Angelegt am 07.04.2014 von N. N
Geändert am 07.04.2014 von N. N
[Edit | Vorlage]