群胚对左消除性小范畴的部分作用的Zappa–Szép乘积

IF 0.7 2区数学 Q2 MATHEMATICS Journal of Noncommutative Geometry Pub Date : 2021-10-12 DOI:10.4171/jncg/518

E. Ortega, E. Pardo

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引用次数: 0

摘要

我们研究左消除剂小范畴上的类群作用及其相关的Zappa-Sz’ep乘积。我们证明了某些具有良好长度函数的左可消小范畴可以看作Zappa-Sz’ep乘积。我们计算了相关的紧群胚，刻画了它们的重要性质，如Hausdorff，有效和极小。最后，在温和合理的假设下，我们确定了紧群胚的可修性。

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Zappa–Szép products for partial actions of groupoids on left cancellative small categories

We study groupoid actions on left cancellative small categories and their associated Zappa-Sz\'ep products. We show that certain left cancellative small categories with nice length functions can be seen as Zappa-Sz\'ep products. We compute the associated tight groupoids, characterizing important properties of them, like being Hausdorff, effective and minimal. Finally, we determine amenability of the tight groupoid under mild, reasonable hypotheses.

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来源期刊

Journal of Noncommutative Geometry 数学-数学

CiteScore

1.60

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Noncommutative Geometry covers the noncommutative world in all its aspects. It is devoted to publication of research articles which represent major advances in the area of noncommutative geometry and its applications to other fields of mathematics and theoretical physics. Topics covered include in particular: Hochschild and cyclic cohomology K-theory and index theory Measure theory and topology of noncommutative spaces, operator algebras Spectral geometry of noncommutative spaces Noncommutative algebraic geometry Hopf algebras and quantum groups Foliations, groupoids, stacks, gerbes Deformations and quantization Noncommutative spaces in number theory and arithmetic geometry Noncommutative geometry in physics: QFT, renormalization, gauge theory, string theory, gravity, mirror symmetry, solid state physics, statistical mechanics.