Leavitt Path Algebras of Edge-Colored Graphs

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• 作者：Hossein Larki (1)
  
• 关键词：16W50 ; 16D70 ; Leavitt path algebra ; Free product ; $${\mathbb{Z}}$$ ; graded ring ; Simplicity
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2013
• 出版时间：November 2013
• 年：2013
• 卷：10
• 期：4
• 页码：1669-1684
• 全文大小：332KB
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• 作者单位：Hossein Larki (1)
  
  1. Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Shahid Chamran University, P.O. Box: 61357-43311, Ahwaz, Iran
  
• ISSN：1660-5454

文摘

Given any edge-colored graph G and any commutative unital ring R, we construct a generalized Leavitt path algebra L R (G).We show that L R (G) is a certain free product of L R (G i ), where G i s are 1-colored subgraphs of G. We also show that L R (G) may be written as a free product of simpler algebras. In the end, we define a natural ${\mathbb{Z}}$ -grading for L R (G) and give four necessary conditions for simplicity of L R (G).