All Questions
7 questions
8
votes
1
answer
601
views
Isomorphism in cyclic cohomology vs isomorphism in Hochschild cohomology
Let $A$ be a unital algebra over a field $K$, $C^n(A)$ a space of all $n+1$ linear maps into scalar field $k$ (I'm interested in case $k=\mathbb{C}$) and
$$(bf)(a_0,...,a_{n+1})=\sum_{i=0}^n(-1)^if(...
- 9,330
7
votes
0
answers
575
views
Why is Hochschild homology interesting if its cohomology groups are infinite-dimensional?
I am trying to understand Hochschild homology, in particular the Hochschild–Kostant–Rosenberg theorem. As far as I understand this result gives an isomorphism between the algebraic (Kähler) ...
- 1,144
5
votes
0
answers
491
views
Soft Question: What does periodic cyclic theory measure?
Ex1) The cyclic homology of $\mathbb{C}[X,Y]$ and that of the algebra of functions on the sphere $S^2$ have the same periodic cyclic homology. Clearly, however, these objects are topologically very ...
- 5,405
4
votes
1
answer
535
views
A Question on Koszul duality and $B(\infty)$ structures on $HH^*$
The following theorem is known from a paper "Duality in Gerstenhaber Algebras" by Felix, Menichi, Thomas. Given a simply connected space X of finite type.
There is an equivalence of Gerstenhaber ...
- 3,758
4
votes
0
answers
211
views
Inner automorphisms acts as identity on Hochschild homology
Let $A$ be a unital algebra and $u \in A$ be an invertible element. Let us consider $u_n(a_0 \otimes a_1 \otimes ... \otimes a_n):=ua_0u^{-1} \otimes ua_1u^{-1} \otimes ... \otimes ua_nu^{-1}$. Then $(...
- 9,330
3
votes
1
answer
817
views
dg-lie structure on $HH^*$ and Koszul duality
This is shamelessly close to my other question: A Question on Koszul duality and $B(\infty)$ structures on $HH^*$. Maybe this one will get a better response. Rather than rewrite that one, I am going ...
- 3,758
1
vote
1
answer
273
views
Jacobi-Zariski exact sequence question
Denote by $HC(A,M)$ the Hochschild homological complex of an algebra $A$ with coefficients in an $A$-bimodule $M$, and let $B\rightarrow A$ be an $R$-flat extension of $R$-algebras, for some $CRing$ $...
- 5,405