Talk:Hochschild homology

Need Motivation and Examples
There needs to be additional motivation and examples for hochschild homology such as computations for artin algebras over a field and the HKR theorem for smooth manifolds/varieties. There should write up a section explaining the relationship of hochschild homology with deformation quantization. Also, it would be nice to discuss the motivic properties with respect to semi-orthogonal decompositions of derived categories, but that would require quite a bit of preperatory articles. — Preceding unsigned comment added by Algebraic geometer (talk • contribs) 05:11, 22 April 2017 (UTC)

It would be more sensible to give the standard usable definition of Hochschild cohomology differential first, rather than starting with Tor and Ext g7c4 16:28, 16 October 2015 (UTC) — Preceding unsigned comment added by G7c4 (talk • contribs)

My hazy (and inexpert) recollection is that the interpretation of Hochschild homology via Loday's construction holds only for commutative unital algebras and symmetric "unit-linked" bimodules. Is there anyone reading, better versed in the relevant details, who could help clarify the corresponding sections of this entry? NowhereDense (talk) 10:14, 27 September 2008 (UTC)

Symmetric bimodule
What is a "symmetric bimodule"? Is it the same as a Krull symmetric bimodule? (I added a request on the page itself, as well.) Dylan Thurston (talk) 02:30, 23 March 2012 (UTC)

A "symmetic bimodule" $M$ is an $R-R$ bimodule such that the left action equals the right action: that is, $rm=mr$ for all $m\in M$ and $r\in R$. — Preceding unsigned comment added by 67.171.213.135 (talk) 18:48, 17 May 2012 (UTC)