Let $V$ is a module over a field $k$, and $A=T(V)$ the tensor algebra generated by $V$. The Hochschild homology $HH_*(A)$ has been determined by Loday and Quillen in their paper "Cyclic homology and the Lie algebra homology of matrices". I was wondering if anything is known about $HH_*(A)$ when $A$ is taken to be $T(V)$ modulo a two-sided ideal $I$, even for something simple such as when $I$ generated by lie brackets $[u,v]$, for some $u,v\in V$?
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13$\begingroup$ All algebras are quotients of tensor algebras, right? $\endgroup$– Fernando MuroCommented Oct 14, 2013 at 12:45
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$\begingroup$ Look at goodwillie's theorem $\endgroup$– ABIMCommented Apr 6, 2014 at 17:29
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