Leavitt path algebras for power graphs of finite groups

摘要

The aim of this paper is the characterization of algebraic properties of Leavitt path algebra of the directed power graph ?(G) and also of the directed punctured power graph ?∗(G) of a finite group G. We show that Leavitt path algebra of the power graph ?(G) of finite group G over a field K is simple if and only if G is a direct sum of finitely many cyclic groups of order 2. Finally, we prove that the Leavitt path algebra LK(?∗(G)) is a prime ring if and only if G is either cyclic p-group or generalized quaternion 2-group.