JACOBI-ZARISKI EXACT SEQUENCE FOR HOCHSCHILD HOMOLOGY AND CYCLIC (CO)HOMOLOGY


Kaygun A.

HOMOLOGY HOMOTOPY AND APPLICATIONS, vol.14, no.1, pp.65-78, 2012 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 1
  • Publication Date: 2012
  • Doi Number: 10.4310/hha.2012.v14.n1.a4
  • Title of Journal : HOMOLOGY HOMOTOPY AND APPLICATIONS
  • Page Numbers: pp.65-78

Abstract

We prove that for an inclusion of unital associative but not necessarily commutative k-algebras B subset of A we have long exact sequences in Hochschild homology and cyclic (co)homology akin to the Jacobi-Zariski sequence in Andre-Quillen homology, provided that the quotient B-module AIB is flat. We also prove that for an arbitrary r-flat morphism phi: B -> 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.