Relative contravariantly finite subcategories and relative tilting modules

2016/12/26 by Han, Wei, Li, Shen, Zhang, Shunhua
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1612.08342

Abstract

Let A be a finite dimensional algebra over an algebraically closed field k. Let T be a tilting A-module and B=\rm End_A T be the endomorphism algebra of T. In this paper, we consider the correspondence between the tilting A-modules and the tilting B-modules, and we prove that there is a one-one correspondence between the basic T-tilting A-modules in T^⊥ and the basic tilting B-modules in ^⊥(D_BT). Moreover, we show that there is a one-one correspondence between the T-contravariantly finite T-resolving subcategories of T^⊥ and the basic T-tilting A-modules contained in T^⊥. As an application, we show that there is a one-one correspondence between the basic tilting A-modules in T^⊥ and the basic tilting B-modules in ^⊥(D_BT) if A is a 1-Gorenstein algebra or a m-replicated algebra over a finite dimensional hereditary algebra.

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