Graded irreducible representations of Leavitt path algebras: A new type and complete classification

We present a new class of graded irreducible representations Leavitt path algebra. This is in the sense that its representation space not isomorphic to any existing simple Chen modules. The corresponding modules complete list which are graded, creating an exhaustive class: annihilator module equal either or this type. Our characterization primitive ideals algebra terms properties underlying graph main tool for proving completeness such classification. also point out problem with [K. M. Rangaswamy, Theory prime algebras over arbitrary graphs, J. Algebra 375 (2013), 73 – 90].