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In the theory of finite dimensional algebras there are many homological conjectures. When working over an algebraically closed field it is well known that any such algebra is Morita equivalent to a quiver algbra $kQ/I$ and thus it is enough to prove such a homological conjecture for quiver algebras. However, there are examples where the conjecture is known for quiver algebras but not for general algebras ,see for example the strong no loop conjecture https://www.sciencedirect.com/science/article/pii/S0001870811002714 .

Question:

Is there a (former) homological conjecture (or theorem/result as you what to call it after it has been proved/disproved) that is known to hold true for quiver algebras but is false for general finite dimensional algebras?

In the theory of finite dimensional algebras there are many homological conjectures. When working over an algebraically closed field it is well known that any such algebra is Morita equivalent to a quiver algbra $kQ/I$ and thus it is enough to prove such a homological conjecture for quiver algebras. However, there are examples where the conjecture is known for quiver algebras but not for general algebras ,see for example the strong no loop conjecture https://www.sciencedirect.com/science/article/pii/S0001870811002714 .

Question:

Is there a homological result (which might have been a conjecture at some point, but not necessarily) that is known to hold true for quiver algebras but is false for general finite dimensional algebras?

In the theory of finite dimensional algebras there are many homological conjectures. When working over an algebraically closed field it is well known that any such algebra is Morita equivalent to a quiver algbra $kQ/I$ and thus it is enough to prove such a homological conjecture for quiver algebras. However, there are examples where the conjecture is known for quiver algebras but not for general algebras ,see for example the strong no loop conjecture https://www.sciencedirect.com/science/article/pii/S0001870811002714 .

Question:

Is there a homological conjecture (or theorem) that is known to hold true for quiver algebras but is false for general finite dimensional algebras?

In the theory of finite dimensional algebras there are many homological conjectures. When working over an algebraically closed field it is well known that any such algebra is Morita equivalent to a quiver algbra $kQ/I$ and thus it is enough to prove such a homological conjecture for quiver algebras. However, there are examples where the conjecture is known for quiver algebras but not for general algebras ,see for example the strong no loop conjecture https://www.sciencedirect.com/science/article/pii/S0001870811002714 .

Question:

Is there a (former) homological conjecture (or theorem/result as you what to call it after it has been proved/disproved) that is known to hold true for quiver algebras but is false for general finite dimensional algebras?