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Let $A$ be a representation-finite quiver algebra and $M$ an indecomposable $A$-module and $s$ the dimension of $A$ and $e_i$ the canonical primitive idempotents. What is the largest possible value (depending on $A$ and $M$) of $T:=\max \{ \dim(M e_i) \}$ /s? Can $T$ be larger than $2$(probably not, maybe even 1 is close to the maximum)? Note that $\dim(M e_i)$ is just the dimension of the vector space at the point $i$.

Example: $T$ is one for $A=K[x]/(x^n)$.

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    $\begingroup$ Maybe I'm misunderstanding what you're asking, but doesn't $T=n$ for $A=K[x]/(x^n)$ (taking $M=A$). $\endgroup$
    – Jeremy Rickard
    Commented Sep 21, 2016 at 15:38
  • $\begingroup$ thanks for the comment. I wanted s to be the dimension of the algebra instead of the number of simples. $\endgroup$
    – Mare
    Commented Sep 21, 2016 at 15:52

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