Leavitt path algebras for order prime Cayley graphs of finite groups

Document Type : Original paper

Authors

Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Kolkata-700019, India

Abstract

In this paper, we generalize the concept of Cayley graphs associated to finite groups. The aim of this paper is the characterization of graph theoretic properties of new type of directed graph ΓP(G;S) and algebraic properties of Leavitt path algebra of order prime Cayley graph OΓ(G;S), where G is a finite group with a generating set S. We show that the Leavitt path algebra of order prime Cayley graph LK(OΓ(G;S)) of a non trivial finite group G with any generating set S over a field K is a purely infinite simple ring. Finally, we prove that the Grothendieck group of the Leavitt path algebra LK(ΓP(Dn;S)) is isomorphic to Z2n−1, where Dn is the dihedral group of degree n and S={a,b} is the generating set of Dn.

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References

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Communications in Combinatorics and Optimization
Volume 10, Issue 4
December 2025
Pages 743-761

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