I am wondering if there is a nice presentation of the Hochschild cohomology of $A_n$ the Weyl algebra. It is known that $H^m(A_n,A_n)=0$ for $m>0$, and thus it is rigid. A proof can be found [in Sridharan][1], but this proof seems to be doing a lot more and is fairly complicated. 

I was wondering if there was a simpler way to see this fact specifically. Essentially, I am being a bit lazy. 

Thanks!


  [1]: http://www.ams.org/journals/tran/1961-100-03/S0002-9947-1961-0130900-1/S0002-9947-1961-0130900-1.pdf