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

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.

In this version, Theorem 4 has been revised for improved clarity. Several typos have been corrected, and some errors in the proofs of various theorems have been fixed