Videos

tau-tilting theory 2

Presenter
November 1, 2012
Keywords:
  • algebraic combinatorics
  • commutative algebra
  • cluster algebra
  • tau-tilting
  • tilting theory
  • quivers
  • representation theory
  • Hasse diagram
  • cluster tilting
MSC:
  • 13F60
  • 13F55
  • 13Fxx
  • 13-xx
  • 05-xx
  • 06-xx
  • 16G70
  • 16G60
  • 16G20
  • 16G10
  • 16Gxx
  • 16-xx
Abstract
These talks are based upon joint work with Adachi, and the first talk is given by Reiten, and the second one is given by Iyama. We introduce and investigate a generalization of classical tilting modules, called (support) tau-tilting modules. For a finite dimensional algebra A over a field, we show that any indecomposable summand of a support tau-tilting A-module can be replaced in a unique way to get a new support tau-tilting A-module. This result is based on a bijection between support tau-tilting A-modules and functorially finite torsion classes in Mod_A. Moreover this gives a natural partial order on the set of support tau-tilting A modules, and we show that the corresponding Hasse quiver coincides with the quiver obtained when mutating tau-tilting modules. We explain how these results were motivated by cluster theory, and how they generalize earlier results on 2-Calabi-Yau triangulated categories. We also explain a connection with tilting theory, in particular with tilting complexes which are two-term.
Supplementary Materials