Zeroth Hochschild homology of preprojective algebras over the integers

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Title: Zeroth Hochschild homology of preprojective algebras over the integers
Author(s): Schedler, T
Item Type: Journal Article
Abstract: We determine the Z-module structure of the preprojective algebra and its zeroth Hochschild homology, for any non-Dynkin quiver (and hence the structure working over any base commutative ring, of any characteristic). This answers (and generalizes) a conjecture of Hesselholt and Rains, producing new p -torsion classes in degrees 2pℓ, ℓ≥1. We relate these classes by p-th power maps and interpret them in terms of the kernel of Verschiebung maps from noncommutative Witt theory. An important tool is a generalization of the Diamond Lemma to modules over commutative rings, which we give in the appendix.
Publication Date: 2-Jun-2016
Date of Acceptance: 16-Feb-2016
ISSN: 1090-2082
Publisher: Elsevier
Start Page: 451
End Page: 542
Journal / Book Title: Advances in Mathematics
Volume: 299
Sponsor/Funder: National Science Foundation
Funder's Grant Number: DMS-1406553
Copyright Statement: © 2016, Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Keywords: General Mathematics
0101 Pure Mathematics
Publication Status: Published
Appears in Collections:Pure Mathematics
Faculty of Natural Sciences

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