| Title:
|
Hochschild cohomology of filtered dg algebras (English) |
| Author:
|
Herscovich, Estanislao |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
4 |
| Issue:
|
2 |
| Year:
|
2020 |
| Pages:
|
167-182 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this article we extend the main result in [15] to the case where the algebra is not necessarily nonnegatively graded connected. More precisely, we show that, for a nonnegatively filtered connected dg algebra $A$, it is possible to compute the cup product of the Hochschild cohomology of $A$ at the level of the complex Hom$_{A^e}(P_\bullet,A)$, where $P_\bullet$ is a semifree resolution of the dg $A$-bimodule $A$ by making use of the coaugmented curved $A_\infty$-coalgebra structure of a suitable Koszul codual of $A$, i.e. a coaugmented curved $A_\infty$-coalgebra $C$ that is filtered quasi-equivalent to the curved bar construction of $A$. We do not need to construct any comparison map between $P_\bullet$ and the Hochschild resolution of $A$, or any lift $\Delta : P \rightarrow P \otimes_{A}P$ of the identity of $A$. (English) |
| Keyword:
|
homological algebra |
| Keyword:
|
dg (co)algebras |
| Keyword:
|
$A_\infty$-(co)algebras |
| MSC:
|
16E05 |
| MSC:
|
16E45 |
| MSC:
|
16T15 |
| MSC:
|
16W70 |
| idZBL:
|
Zbl 1473.16002 |
| idMR:
|
MR4133166 |
| DOI:
|
10.21136/HS.2020.12 |
| . |
| Date available:
|
2026-03-12T13:53:48Z |
| Last updated:
|
2026-03-12 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153428 |
| . |
| Reference:
|
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| . |
