Given a finite dimensional selfinjective algebra $A$. By definition, the period of $A$ is the smallest integer $i >0$ such that $\Omega^{i}(A) \cong A$ as $A \otimes_K A^{op}$-modules. Is the period of a periodic algebra with $n$ simples bounded by a function depending on $n$? To be more concrete lets try the following: Is the period of a periodic algebra with n simples bounded by 100n+100? What is the highest period of a local algebra you are aware of? (are the local periodic algebras classified?)
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