颤振和轮条件的洗牌代数

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2022-12-01 DOI:10.1515/crelle-2022-0074
Andrei Neguț
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引用次数: 1

摘要

摘要本文证明了由最小次元生成的双颤振(由3变量轮条件决定)的洗牌代数。结合Varagnolo-Vasserot和Yu Zhao的结果,这表明上述洗牌代数与Grojnowski、Schiffmann-Vasserot和Yang-Zhao的与抖动相关的局域化𝐾-theoretic Hall代数是同构的。稍加修改,我们的定理也适用于等变参数的某些专门化,这将允许我们与Sala和Schiffmann共同工作,给出有限域上任何曲线的霍尔代数的生成和关系描述(这是由于Kapranov-Schiffmann-Vasserot的洗牌代数)。当颤抖器没有边缘环或多条边时,我们证明了shuffle代数、局域𝐾-theoretic Hall代数和对应的量子环群的正半部分都是同构的;得到了Hopf对在后一量子环群上的非简并性。
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Shuffle algebras for quivers and wheel conditions
Abstract We show that the shuffle algebra associated to a doubled quiver (determined by 3-variable wheel conditions) is generated by elements of minimal degree. Together with results of Varagnolo–Vasserot and Yu Zhao, this implies that the aforementioned shuffle algebra is isomorphic to the localized 𝐾-theoretic Hall algebra associated to the quiver by Grojnowski, Schiffmann–Vasserot and Yang–Zhao. With small modifications, our theorems also hold under certain specializations of the equivariant parameters, which will allow us in joint work with Sala and Schiffmann to give a generators-and-relations description of the Hall algebra of any curve over a finite field (which is a shuffle algebra due to Kapranov–Schiffmann–Vasserot). When the quiver has no edge loops or multiple edges, we show that the shuffle algebra, localized 𝐾-theoretic Hall algebra, and the positive half of the corresponding quantum loop group are all isomorphic; we also obtain the non-degeneracy of the Hopf pairing on the latter quantum loop group.
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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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