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YCor
YCor
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A representation-directed algebra $A$ over a field $K$ has the property that for every indecomposable module $M$ we have $End_A(M) \cong k$$\mathrm{End}_A(M) \cong K$ and $Ext_A^i(M,M)=0$$\mathrm{Ext}_A^i(M,M)=0$ for all $i>0$.

Question: In case for every indecomposable module $M$ we have $End_A(M) \cong k$$\mathrm{End}_A(M) \cong K$ and $Ext_A^i(M,M)=0$$\mathrm{Ext}_A^i(M,M)=0$ for all $i>0$, is $A$ representation-directed? Is it true under the additional assumption that $A$ is representation-finite?

A representation-directed algebra $A$ over a field $K$ has the property that for every indecomposable module $M$ we have $End_A(M) \cong k$ and $Ext_A^i(M,M)=0$ for all $i>0$.

Question: In case for every indecomposable module $M$ we have $End_A(M) \cong k$ and $Ext_A^i(M,M)=0$ for all $i>0$, is $A$ representation-directed? Is it true under the additional assumption that $A$ is representation-finite?

A representation-directed algebra $A$ over a field $K$ has the property that for every indecomposable module $M$ we have $\mathrm{End}_A(M) \cong K$ and $\mathrm{Ext}_A^i(M,M)=0$ for all $i>0$.

Question: In case for every indecomposable module $M$ we have $\mathrm{End}_A(M) \cong K$ and $\mathrm{Ext}_A^i(M,M)=0$ for all $i>0$, is $A$ representation-directed? Is it true under the additional assumption that $A$ is representation-finite?

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Mare
Mare
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Characterisation of representation-directed algebras

A representation-directed algebra $A$ over a field $K$ has the property that for every indecomposable module $M$ we have $End_A(M) \cong k$ and $Ext_A^i(M,M)=0$ for all $i>0$.

Question: In case for every indecomposable module $M$ we have $End_A(M) \cong k$ and $Ext_A^i(M,M)=0$ for all $i>0$, is $A$ representation-directed? Is it true under the additional assumption that $A$ is representation-finite?