Jacobi-Zariski Exact Sequence for Hochschild Homology and Cyclic (Co)Homology

Abstract

We prove that for an inclusion of unital associative but not necessarily commutative algebras $B\subseteq A$ 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 $B$-bimodule $A/B$ is flat. We also prove that for an arbitrary r-flat morphism $f:B\to A$ with an H-unital kernel, one can express the Wodzicki excision sequence and the corresponding Jacobi-Zariski sequence in Hochschild homology and cyclic (co)homology as a single long exact sequence.

The current version corrects the range for which the Jacobi-Zariski long exact sequence holds. An errata for the published version is to appear

Cited by in corpus (7)

• Split bounded extension algebras and Han's conjecture
• Jacobi-Zariski long nearly exact sequences for associative algebras
• Cyclic Homology and Quantum Orbits
• Noncommutative Fibrations
• Han's conjecture for bounded extensions
• Hochschild Cohomology of Reduced Incidence Algebras
• A characteristic map for compact quantum groups