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

Kaygun A.

HOMOLOGY HOMOTOPY AND APPLICATIONS, cilt.14, sa.1, ss.65-78, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 1
  • Basım Tarihi: 2012
  • Doi Numarası: 10.4310/hha.2012.v14.n1.a4
  • Dergi Adı: HOMOLOGY HOMOTOPY AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.65-78
  • İstanbul Teknik Üniversitesi Adresli: Hayır

Özet

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.