Zeroth Hochschild homology of preprojective algebras over the integers
File(s)
Accepted version
Author(s)
Schedler, T
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.
Date Issued
2016-06-02
Date Acceptance
2016-02-16
Citation
Advances in Mathematics, 2016, 299, pp.451-542
ISSN
1090-2082
Publisher
Elsevier
Start Page
451
End Page
542
Journal / Book Title
Advances in Mathematics
Volume
299
Copyright Statement
© 2016, Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Sponsor
National Science Foundation
Grant Number
DMS-1406553
Subjects
General Mathematics
0101 Pure Mathematics
Publication Status
Published