Geodesic
Cyclic $A_\infty$-algebras and cyclic homology
Homology, homotopy, and applications, Tome 25 (2023) no. 1, pp. 287-318.

Voir la notice de l'article provenant de la source International Press of Boston

We provide a new description of the complex computing the Hochschild homology of an $H$-unitary $A_\infty$-algebra $A$ as a derived tensor product $A \oplus^\infty_{A^\epsilon}$ such that: (1) there is a canonical morphism from it to the complex computing the cyclic homology of $A$ that was introduced by Kontsevich and Soibelman, (2) this morphism induces the map $I$ in the well-known SBI sequence, and (3) $H^0 \left( (A \oplus^\infty_{A^\epsilon} A)^\# \right)$ is canonically isomorphic to the space of morphisms from $A$ to $A^\#$ in the derived category of $A_\infty$-bimodules. As direct consequences we obtain previous results of Cho and Cho–Lee, as well as the fact that Koszul duality establishes a bijection between (resp., almost exact) $d$-Calabi–Yau structures and (resp., strong) homotopy inner products, extending a result proved by Van den Bergh.
DOI : 10.4310/HHA.2023.v25.n1.a15
Classification : 16E05, 16E40, 16E45, 16T15
Keywords: dg (co)algebra, $A_\infty$-algebra, Calabi–Yau, Koszul duality 
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     author = {Estanislao Herscovich},
     title = {Cyclic $A_\infty$-algebras and cyclic homology},
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     pages = {287--318},
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     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2023.v25.n1.a15/}
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Estanislao Herscovich. Cyclic $A_\infty$-algebras and cyclic homology. Homology, homotopy, and applications, Tome 25 (2023) no. 1, pp. 287-318. doi : 10.4310/HHA.2023.v25.n1.a15. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2023.v25.n1.a15/

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