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

Pub Date : 2024-04-09 DOI:10.1007/s00013-024-01975-1
Promit Mukherjee, Sujit Kumar Sardar
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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。)
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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 \(L_S(\Gamma )\).

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