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5 votes
1 answer
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Hochschild homology of a category of modules over an algebra

Suppose $A$ is an algebra over some field, say the complex numbers if that helps. Then we can consider the category $\mathbf{C}_A$ of finite-dimensional modules over $A$. This category can be seen as ...
Lukas Woike's user avatar
  • 1,382
4 votes
2 answers
760 views

What is the homology of the real coordinate ring of SO(n,R)? Other compact matrix groups?

As someone whose knowledge of cohomology is patchy and picked up on a need-to-know basis, and whose algebraic geometry is even worse, I wondered if someone could help with this question. (I ran into ...
Yemon Choi's user avatar
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1 vote
0 answers
147 views

Simplicial realization of the circle action on the free loop space

Given a simply connected topological space $X$, it is well known that its free loop space $LX$ has cohomology being the Hochschild homology of the singular cochains [1]: $$HH_\bullet(S^\star X) \simeq ...
Student's user avatar
  • 5,230