Noncommutative fibrations

Atabey Kaygun*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We show that faithfully flat smooth extensions of associative unital algebras are reduced flat, and therefore, fit into the Jacobi-Zariski exact sequence in Hochschild homology and cyclic (co)homology even when the algebras are noncommutative or infinite dimensional. We observe that such extensions correspond to étale maps of affine schemes, and we propose a definition for generic noncommutative fibrations using distributive laws and homological properties of the induction and restriction functors. Then we show that Galois fibrations do produce the right exact sequence in homology. We then demonstrate the versatility of our model on a geometro-combinatorial example. For a connected unramified covering of a connected graph G' → G, we construct a smooth Galois fibration (Formula presented.) and calculate the homology of the corresponding local coefficient system.

Original languageEnglish
Pages (from-to)3384-3398
Number of pages15
JournalCommunications in Algebra
Volume47
Issue number8
DOIs
Publication statusPublished - 3 Aug 2019

Bibliographical note

Publisher Copyright:
© 2019, © 2019 Taylor & Francis Group, LLC.

Keywords

  • algebra extensions
  • Hochschild homology
  • Jacobi-Zariski
  • noncommutative algebras

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