Geodesic
Jacobi-Zariski exact sequence for Hochschild homology and cyclic (co)homology
Homology, homotopy, and applications, Tome 14 (2012) no. 1, pp. 65-78.

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

We prove that for an inclusion of unital associative but not necessarily commutative $\Bbbk$-algebras $\mathcal{B}\subseteq \mathcal{A}$ we have long exact sequences in Hochschild homology and cyclic (co)homology akin to the Jacobi-Zariski sequence in André-Quillen homology, provided that the quotient $\mathcal{B}$-module $\mathcal{A}/\mathcal{B}$ is flat. We also prove that for an arbitrary r-flat orphism $\varphi\colon\mathcal{B}\to\mathcal{A}$ with an H-unital kernel, one can express the Wodzicki excision sequence and our Jacobi-Zariski sequence in Hochschild homology and cyclic (co)homology as a single long exact sequence.
DOI : 10.4310/HHA.2012.v14.n1.a4
Classification : 16W70, 18G25, 18G40, 19D55
Keywords: Jacobi-Zariski sequence, excision, Hochschild homology, cyclic cohomology 
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     author = {Atabey Kaygun},
     title = {Jacobi-Zariski exact sequence for {Hochschild} homology and cyclic (co)homology},
     journal = {Homology, homotopy, and applications},
     pages = {65--78},
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     year = {2012},
     doi = {10.4310/HHA.2012.v14.n1.a4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2012.v14.n1.a4/}
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Atabey Kaygun. Jacobi-Zariski exact sequence for Hochschild homology and cyclic (co)homology. Homology, homotopy, and applications, Tome 14 (2012) no. 1, pp. 65-78. doi : 10.4310/HHA.2012.v14.n1.a4. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2012.v14.n1.a4/

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