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

摘要

We prove that for an inclusion of unital associative but not necessarilycommutative algebras $B\subseteq A$ we have long exact sequences in Hochschildhomology and cyclic (co)homology akin to the Jacobi-Zariski sequence inAndr\'e-Quillen homology, provided that the quotient $B$-module $A/B$ is flat.We also prove that for an arbitrary r-flat morphism $f:B\to A$ with an H-unitalkernel, one can express the Wodzicki excision sequence and the correspondingJacobi-Zariski sequence in Hochschild homology and cyclic (co)homology as asingle long exact sequence.