# 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