2018-03-22 16:43:09 8 Comments

Let $A$ be a Hopf algebra over the complex numbers. Denote by $\mathcal{M}$ the dg-category of dg-$A$-modules. The Hochschild homology of $\mathcal{M}$ is not going to be the Hochschild homology of $A$, but can I compute the Hochschild homology of $A$ as the Hochschild homology of a subcategory of $\mathcal{M}$, preferrably some subcategory of objects which are dualizable?

I know that I can take perfect modules, but this subcategory, for instance, might not contain the tensor unit of $\mathcal{M}$, which might be a problem.

In summary, my question is what are the dg-categories built from $A$ and its modules whose Hochschild homology gives me the Hochschild homology of $A$?

### Related Questions

#### Sponsored Content

#### 1 Answered Questions

### [SOLVED] Do the "funny" tensor product and the cartesian product satisfy any algebraic "laws"?

**2012-07-23 08:08:19****Harry Gindi****1173**View**10**Score**1**Answer- Tags: ct.category-theory

#### 1 Answered Questions

### [SOLVED] Is K theory ever trivial because of the ring, and not because of the kinds of modules we look at?

**2018-03-19 19:00:56****KTheoryYayTheory****418**View**11**Score**1**Answer- Tags: ct.category-theory kt.k-theory-and-homology

#### 1 Answered Questions

### [SOLVED] How nontrivial can "central extensions of ribbon fusion categories" be?

**2016-05-05 16:03:37****Manuel Bärenz****115**View**2**Score**1**Answer- Tags: ct.category-theory fusion-categories braided-tensor-categories symmetric-monoidal-categories modular-tensor-categories

#### 1 Answered Questions

### [SOLVED] Gauss Sums over "semisimple spherical tensor category"?

**2014-05-30 14:01:18****john mangual****236**View**0**Score**1**Answer- Tags: nt.number-theory at.algebraic-topology ct.category-theory

#### 2 Answered Questions

### [SOLVED] Dualizable objects are flat?

**2011-06-24 10:47:48****Martin Brandenburg****948**View**8**Score**2**Answer- Tags: ag.algebraic-geometry ct.category-theory

## 0 comments