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Tagged with hochschild-homology noncommutative-algebra
8 questions
3
votes
1
answer
280
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Hochschild homology of acyclic complex
Let $A$ be a differential graded algebra over a commutative ring $R$. Suppose that $H_*(A)=0$, i.e. $A$ is acyclic.
Question: Does this imply that the Hochschild homology $HH_*(A)$ also vanishes ...
- 177
1
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0
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60
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Universal bimodule for homotopy biderivations
Recall the commutative story: for a commutative algebra $A$, its module of differentials $\Omega (A)$ is characterized by the universal property that any derivation $\delta \colon A \to M$ is in a ...
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8
votes
2
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721
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Hochschild homology of upper triangular matrix algebra?
Let $K$ be a field and $A$ the associative unital $K$-algebra of all $n\times n$ upper triangular matrices with entries in $K$. What is $\dim_K$ of its hochschild homology $HH_k(A;A)$?
Is there any ...
- 1,589
3
votes
0
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169
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Hochschild homology and Chern character quiver with potential
I am a beginner in quiver theory so this question might not be suitable for mathoverflow.
Let $(Q,W)$ be a quiver with potential and let $\Gamma$ be the Ginzburg DG-algebra associated to $(Q,W)$. Is ...
- 7,320
6
votes
1
answer
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Hochschild homology of quiver algebras
Let $K$ be a field and $\Gamma$ a quiver (=multidigraph) and $K[\Gamma]$ its quiver algebra (free $K$-module on the set of all paths of length $\geq0$ where multiplication is concatenation if ...
- 1,589
2
votes
1
answer
578
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Interpretation of Hochschild Homology groups
In all the literature I've come across there are many concrete interpretations of the first few Hochschild Cohomology groups. For example $HH^1(A,M)\cong Derivation/Inner Derivations$ etc....
In ...
- 5,405
1
vote
1
answer
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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
2
votes
0
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90
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Poincaré Duality of a quasi-free algebra
I'm completely stumped on this one (yet I feel it is obviously true or obviously false)
If $A$ is a quasi-free algebra, then must it satisfy Poincaré duality?
All i need to find is a protective ...
