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 language | English |
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Pages (from-to) | 3384-3398 |
Number of pages | 15 |
Journal | Communications in Algebra |
Volume | 47 |
Issue number | 8 |
DOIs | |
Publication status | Published - 3 Aug 2019 |
Bibliographical note
Publisher Copyright:© 2019, © 2019 Taylor & Francis Group, LLC.
Keywords
- algebra extensions
- Hochschild homology
- Jacobi-Zariski
- noncommutative algebras