Given a finite dimensional algebra A such that the regular module embeds into a projective-injective module (such algebras are called QF-3 algebras and generalise Frobenius algebras).

Define the finitistic dimension findim(A) of A as the supremum of projective dimensions of modules having finite projective dimension.

Question:Is the finitistic dimension of $A$ equal to the finitistic dimension of the opposite algebra $A^{op}$?

I see no reason, but some random tests gave no counterexamples to my surprise.

  • $\begingroup$ If you're considering left $A$-modules, then by duality your co-finitistic dimension should coincide with the right finitisitic dimension of $A$. There are many examples where the left and right finitistic dimension are different, but I don't know yet if any satisfy your additional condition. $\endgroup$ – Alex Dugas Jan 30 '17 at 21:57

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.