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- W1627338865 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 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 $text{Sym } HH_0(Pi)$ for all quivers, the BV algebra structure on Hochschild cohomology, including how the Lie algebra structure $HH_0(Pi_Q)$ naturally arises from it, and the cyclic homology groups of $Pi_Q$." @default.
- W1627338865 created "2016-06-24" @default.
- W1627338865 creator A5076809544 @default.
- W1627338865 date "2007-04-24" @default.
- W1627338865 modified "2023-09-27" @default.
- W1627338865 title "Zeroth Hochschild homology of preprojective algebras over the integers" @default.
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