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Let algebras always be finite dimensional connected non-semisimple quiver algebras. Say an algebra $A$ has property * in case $eAe$ is a Nakayama algebra, when $eA$ denotes the basic version of the direct sum of all indecomposable projective-injective modules. Is there a nice other characterisation of algebras having property *? This class of algebras seems to contain several large classes such as:   

-monomial algebras   

-Algebras with no projective-injective module. Are

Are there other large known classes of algebras having property *?

Let algebras always be finite dimensional connected non-semisimple quiver algebras. Say an algebra $A$ has property * in case $eAe$ is a Nakayama algebra, when $eA$ denotes the basic version of the direct sum of all indecomposable projective-injective modules. Is there a nice other characterisation of algebras having property *? This class of algebras seems to contain several large classes such as:  -monomial algebras  -Algebras with no projective-injective module. Are there other large known classes of algebras having property *?

Let algebras always be finite dimensional connected non-semisimple quiver algebras. Say an algebra $A$ has property * in case $eAe$ is a Nakayama algebra, when $eA$ denotes the basic version of the direct sum of all indecomposable projective-injective modules. Is there a nice other characterisation of algebras having property *? This class of algebras seems to contain several large classes such as: 

-monomial algebras 

-Algebras with no projective-injective module.

Are there other large known classes of algebras having property *?

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Mare
Mare
  • 26.5k
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  • 25
  • 104

Characterisation of certain quiver algebras

Let algebras always be finite dimensional connected non-semisimple quiver algebras. Say an algebra $A$ has property * in case $eAe$ is a Nakayama algebra, when $eA$ denotes the basic version of the direct sum of all indecomposable projective-injective modules. Is there a nice other characterisation of algebras having property *? This class of algebras seems to contain several large classes such as: -monomial algebras -Algebras with no projective-injective module. Are there other large known classes of algebras having property *?