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Hi, let A be a finite dimensional selfinjective algebra. Assume mod A is periodic.That is for every finite dimensional module with no projective summand we have: $\Omega^{n} (M) =M$ for some n ,where $\Omega$ is the Hellerfunctor(giving the kernel of a projective cover of M ). When is it true that $\Omega$ is of finite order,that is $\Omega^{n}$ is isomorphic as a functor to the identity functor of the stable category of modules without a projective direct summand?(Assume ?(Assume there is a common biggest period for all module if necassary)

Thanks for help

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heller functor of finite order

Hi, let A be a finite dimensional selfinjective algebra. Assume mod A is periodic.That is for every finite dimensional module with no projective summand we have: $\Omega^{n} (M) =M$ for some n ,where $\Omega$ is the Hellerfunctor(giving the kernel of a projective cover of M ). When is it true that $\Omega$ is of finite order,that is $\Omega^{n}$ is isomorphic as a functor to the identity functor of the category of modules without a projective direct summand?(Assume there is a common biggest period for all module if necassary)

Thanks for help