Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. 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

Could someone explain to me how one can compute Hochschild homology of Weyl algebra $A_n$ (i.e. algebra of differential operators with polynomial coefficients in $n$ variables)?

share|cite|improve this question
up vote 5 down vote accepted

I'm surprised that Mariano hasn't replied. The cohomological version of this question has been asked on MO and answered by Mariano:

I think the answer you want is that $$HH_*(A_n(k)) = \begin{cases} 0 &\text{ if } \ast \ne 2n \\ k &\text{ if } \ast=2n\end{cases}$$

The reference is a paper of Sridharan:

And since I haven't yet included enough links here is another paper:

share|cite|improve this answer
Heh. Despite appearances, I am not online all the time :) – Mariano Suárez-Alvarez Mar 2 '12 at 1:22
Thanks, Mariano's answer on mathoverflow is nice, but is it really easier to proof that $A_n$ is CY then directly calculate Hochschild homology? – Alex Mar 5 '12 at 1:25

Your Answer


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

Not the answer you're looking for? Browse other questions tagged or ask your own question.