{"title":"\\(C^*\\) Completions of Leavitt-Path-Algebra Pullbacks","authors":"Alexandru Chirvasitu","doi":"10.1007/s10485-022-09685-x","DOIUrl":null,"url":null,"abstract":"<div><p>We show that certain pullbacks of <span>\\(*\\)</span>-algebras equivariant with respect to a compact group action remain pullbacks upon completing to <span>\\(C^*\\)</span>-algebras. This unifies a number of results in the literature on graph algebras, showing that pullbacks of Leavitt path algebras lift automatically to pullbacks of the corresponding graph <span>\\(C^*\\)</span>-algebras.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2022-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Categorical Structures","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10485-022-09685-x","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
We show that certain pullbacks of \(*\)-algebras equivariant with respect to a compact group action remain pullbacks upon completing to \(C^*\)-algebras. This unifies a number of results in the literature on graph algebras, showing that pullbacks of Leavitt path algebras lift automatically to pullbacks of the corresponding graph \(C^*\)-algebras.
期刊介绍：
Applied Categorical Structures focuses on applications of results, techniques and ideas from category theory to mathematics, physics and computer science. These include the study of topological and algebraic categories, representation theory, algebraic geometry, homological and homotopical algebra, derived and triangulated categories, categorification of (geometric) invariants, categorical investigations in mathematical physics, higher category theory and applications, categorical investigations in functional analysis, in continuous order theory and in theoretical computer science. In addition, the journal also follows the development of emerging fields in which the application of categorical methods proves to be relevant.
Applied Categorical Structures publishes both carefully refereed research papers and survey papers. It promotes communication and increases the dissemination of new results and ideas among mathematicians and computer scientists who use categorical methods in their research.
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