Zeroth Hochschild homology of preprojective algebras over the integers

详细信息    查看全文

• 作者：Travis Schedler ^{trasched@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Hochschild homology ; Preprojective algebra ; Witt ring ; Verschiebung map ; RCI algebra ; NCCI algebra ; Diamond Lemma
• 刊名：Advances in Mathematics
• 出版年：2016
• 出版时间：20 August 2016
• 年：2016
• 卷：299
• 期：Complete
• 页码：451-542
• 全文大小：1393 K

文摘

We determine the Z$\mathbb{Z}$-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$2p^{\ell }$, ℓ≥1$\ell \ge 1$. 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.