MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let A = c[Q]/I be a finite dimensional quotient of a path algebra over a quiver Q, with I being the ideal of relations.

Is it true that the I-adic completion of A has finite homological dimension?

share|cite|improve this question
Do you really mean the $I$-adic completion of $A$, or do you mean the $I$-adic completion of $c[Q]$? (The ideal $I$ "becomes zero" in the factor algebra $A$.) – Manny Reyes Jul 31 '13 at 14:44
To continue Manny's question, another thing you might mean is: the completion of A with respect to the ideal of all arrows. That is the completion which I have seen used (e.g., in representations of quivers with potential). – Hugh Thomas Aug 15 '13 at 4:53
You're right: I meant the I-adic completion of c[Q]. – user41521 Oct 18 '13 at 18:47

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.