{"title":"克利福德半场上的斯坦伯格代数的全 k-简约性及其在 Leavitt 路径代数中的应用","authors":"Promit Mukherjee, Sujit Kumar Sardar","doi":"10.1007/s00013-024-01975-1","DOIUrl":null,"url":null,"abstract":"<div><p>As a continuation of the study of the Steinberg algebra of a Hausdorff ample groupoid <span>\\({\\mathcal {G}}\\)</span> over commutative semirings by Nam et al. (J. Pure Appl. Algebra 225, 2021), we consider here the Steinberg algebra <span>\\(A_S({\\mathcal {G}})\\)</span> with coefficients in a Clifford semifield <i>S</i>. We obtain a complete characterization of the full <i>k</i>-ideal simplicity of <span>\\(A_S({\\mathcal {G}})\\)</span>. Using this result for the Steinberg algebra <span>\\(A_S({\\mathcal {G}}_\\Gamma )\\)</span> of the graph groupoid <span>\\({\\mathcal {G}}_\\Gamma \\)</span>, where <span>\\(\\Gamma \\)</span> is a row-finite digraph and <i>S</i> is a Clifford semifield, we characterize the full <i>k</i>-simplicity of the Leavitt path algebra <span>\\(L_S(\\Gamma )\\)</span>.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Full k-simplicity of Steinberg algebras over Clifford semifields with application to Leavitt path algebras\",\"authors\":\"Promit Mukherjee, Sujit Kumar Sardar\",\"doi\":\"10.1007/s00013-024-01975-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>As a continuation of the study of the Steinberg algebra of a Hausdorff ample groupoid <span>\\\\({\\\\mathcal {G}}\\\\)</span> over commutative semirings by Nam et al. (J. Pure Appl. Algebra 225, 2021), we consider here the Steinberg algebra <span>\\\\(A_S({\\\\mathcal {G}})\\\\)</span> with coefficients in a Clifford semifield <i>S</i>. We obtain a complete characterization of the full <i>k</i>-ideal simplicity of <span>\\\\(A_S({\\\\mathcal {G}})\\\\)</span>. Using this result for the Steinberg algebra <span>\\\\(A_S({\\\\mathcal {G}}_\\\\Gamma )\\\\)</span> of the graph groupoid <span>\\\\({\\\\mathcal {G}}_\\\\Gamma \\\\)</span>, where <span>\\\\(\\\\Gamma \\\\)</span> is a row-finite digraph and <i>S</i> is a Clifford semifield, we characterize the full <i>k</i>-simplicity of the Leavitt path algebra <span>\\\\(L_S(\\\\Gamma )\\\\)</span>.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-04-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00013-024-01975-1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00013-024-01975-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
作为 Nam 等人 (J. Pure Appl. Algebra 225, 2021) 对交换半影上的 Hausdorff 广群 \({\mathcal {G}}\) 的斯坦伯格代数研究的延续,我们在此考虑具有克利福德半影中系数的斯坦伯格代数 \(A_S({\mathcal {G}}\)。我们得到了 \(A_S({\mathcal {G}})\ 的全 k 边简单性的完整表征。使用这个结果来描述图群 \({\mathcal {G}}_\Gamma \)的斯坦伯格代数 \(A_S({\mathcal {G}}_\Gamma ),其中 \(\Gamma \)是一个行inite digraph,而 S 是一个克利福德半域,我们就可以描述 Leavitt 路径代数 \(L_S(\Gamma )\) 的全 k 边简单性。)
Full k-simplicity of Steinberg algebras over Clifford semifields with application to Leavitt path algebras
As a continuation of the study of the Steinberg algebra of a Hausdorff ample groupoid \({\mathcal {G}}\) over commutative semirings by Nam et al. (J. Pure Appl. Algebra 225, 2021), we consider here the Steinberg algebra \(A_S({\mathcal {G}})\) with coefficients in a Clifford semifield S. We obtain a complete characterization of the full k-ideal simplicity of \(A_S({\mathcal {G}})\). Using this result for the Steinberg algebra \(A_S({\mathcal {G}}_\Gamma )\) of the graph groupoid \({\mathcal {G}}_\Gamma \), where \(\Gamma \) is a row-finite digraph and S is a Clifford semifield, we characterize the full k-simplicity of the Leavitt path algebra \(L_S(\Gamma )\).