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2012 Jacobi-Zariski exact sequence for Hochschild homology and cyclic (co)homology
Atabey Kaygun
Homology Homotopy Appl. 14(1): 65-78 (2012).

Abstract

We prove that for an inclusion of unital associative but not necessarily commutative $\mathbb{k}$-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 morphism $\varphi\colon\mathcal{B}\to\mathcal{A}$ 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.

Citation

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Atabey Kaygun. "Jacobi-Zariski exact sequence for Hochschild homology and cyclic (co)homology." Homology Homotopy Appl. 14 (1) 65 - 78, 2012.

Information

Published: 2012
First available in Project Euclid: 12 December 2012

zbMATH: 1259.19003
MathSciNet: MR2954667

Subjects:
Primary: 16W70 , 18G25 , 18G40 , 19D55

Keywords: cyclic cohomology , excision , Hochschild homology , Jacobi-Zariski sequence

Rights: Copyright © 2012 International Press of Boston

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Vol.14 • No. 1 • 2012
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