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On the relation between maximal rigid objects and τ-tilting modules

Pin Liu, Yunli Xie (2016)

Colloquium Mathematicae

This note compares τ-tilting modules and maximal rigid objects in the context of 2-Calabi-Yau triangulated categories. Let be a 2-Calabi-Yau triangulated category with suspension functor S. Let R be a maximal rigid object in and let Γ be the endomorphism algebra of R. Let F be the functor H o m ( R , - ) : m o d Γ . We prove that any τ-tilting module over Γ lifts uniquely to a maximal rigid object in via F, and in turn, that projection from to mod Γ sends the maximal rigid objects which have no direct summands from add...

On the representation type of tensor product algebras

Zbigniew Leszczyński (1994)

Fundamenta Mathematicae

The representation type of tensor product algebras of finite-dimensional algebras is considered. The characterization of algebras A, B such that A ⊗ B is of tame representation type is given in terms of the Gabriel quivers of the algebras A, B.

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