# Which class of finite dimension algebra has only trivial tilting modules?

I have already knowed that selfinjective algebras have only trivial tilting modules,but besides this,is there any more?

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Do you allow $\rm{pd}(T)<\infty$ or only $\rm{pd}(T) \leq 1$? – Dag Oskar Madsen Oct 26 '12 at 6:37

## 1 Answer

Local finite dimensional algebras have only trivial tilting modules since in that case all finitely generated modules have either zero or infinite projective dimension.

In particular it follows that commutative finite dimensional algebras have only trivial tilting modules.

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