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Zeroth Hochschild homology of preprojective algebras over the integers
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
-torsion classes in degrees 2p^l, 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.
In the previous version, additional results are included, such as: the
Poisson center of for all quivers, the BV algebra
structure on Hochschild cohomology, including how the Lie algebra structure
naturally arises from it, and the cyclic homology groups of
.Comment: 69 pages, 2 figures; final pre-publication version; many corrections
and improvements throughout. Note though the first version has additional
results (for instance, it computes the higher Hochschild (co)homology and its
structures
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