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 .


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?

  • By definition, the answer to your question about conjectures is NO. – Fernando Muro Sep 14 at 13:41
  • I changed the question a bit. – Mare Sep 14 at 17:45

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