Cohn Path Algebras of Higher-Rank Graphs

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• 作者：Lisa Orloff Clark ; Yosafat E. P. Pangalela
• 关键词：Cohn path algebra ; Kumjian ; Pask algebra ; Finitely aligned k ; graph ; Steinberg algebra
• 刊名：Algebras and Representation Theory
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：20
• 期：1
• 页码：47-70
• 全文大小：
• 刊物主题：Commutative Rings and Algebras; Associative Rings and Algebras; Non-associative Rings and Algebras;
• 出版者：Springer Netherlands
• ISSN：1572-9079
• 卷排序：20

文摘

In this article, we introduce Cohn path algebras of higher-rank graphs. We prove that for a higher-rank graph Λ, there exists a higher-rank graph T Λ such that the Cohn path algebra of Λ is isomorphic to the Kumjian-Pask algebra of T Λ. We then use this isomorphism and properties of Kumjian-Pask algebras to study Cohn path algebras. This includes proving a uniqueness theorem for Cohn path algebras.