Grothendieck group of the Leavitt path algebra over power graphs of prime-power cyclic groups

Güçlükan İlhan A., Kanuni M., Şimşek E.

Linear Algebra and Its Applications, vol.723, pp.58-77, 2025 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 723
  • Publication Date: 2025
  • Doi Number: 10.1016/j.laa.2025.05.021
  • Journal Name: Linear Algebra and Its Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, MathSciNet, zbMATH
  • Page Numbers: pp.58-77
  • Keywords: Grothendieck group, Leavitt path algebra, Directed power graph, Circulant matrix
  • Dokuz Eylül University Affiliated: Yes

Abstract

In this paper, the Grothendieck group of the Leavitt path algebra over the power graphs of all prime-power cyclic groups is studied by using a well-known computation from linear algebra. More precisely, the Smith normal form of the matrix derived from the adjacency matrix associated with the power graph of prime-power cyclic group is calculated.