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A graph inverse semigroup \(I(\Gamma )\) is a semigroup constructed from a directed graph \({\Gamma }\) , where, roughly speaking, elements correspond to paths in the graph. The main purpose of this overview is to give an introduction to the basic research of graph inverse semigroups including Green’s relations, idempotents, isomorphisms, congruences, and subsemigroups. In addition, this chapter also gives a short note to state much more research perspectives such as the connection with Cuntz-Krieger algebras, the connection with Leavitt path algebras, and the topological structures. This overview is not, of course, a comprehensive one.

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On Graph Inverse Semigroups

  • 章节

  • 发表日期：

    2025年

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  • Yanhui Wang,
  • Zhengpan Wang

摘要

A graph inverse semigroup \(I(\Gamma )\) is a semigroup constructed from a directed graph \({\Gamma }\) , where, roughly speaking, elements correspond to paths in the graph. The main purpose of this overview is to give an introduction to the basic research of graph inverse semigroups including Green’s relations, idempotents, isomorphisms, congruences, and subsemigroups. In addition, this chapter also gives a short note to state much more research perspectives such as the connection with Cuntz-Krieger algebras, the connection with Leavitt path algebras, and the topological structures. This overview is not, of course, a comprehensive one.