{"title":"Zappa–Szép products for partial actions of groupoids on left cancellative small categories","authors":"E. Ortega, E. Pardo","doi":"10.4171/jncg/518","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2021-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Noncommutative Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/jncg/518","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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.
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