On induced graded simple modules over graded Steinberg algebras with applications to Leavitt path algebras

For an ample groupoid [Formula: see text] and a unit of text], Steinberg constructed the induction restriction functors between category modules over algebra isotropy group text]. In this paper, we prove graded version these give description spectral simple As application, Leavitt path are classified. particular, show that many previously known text]-modules, including Chen modules, induced from (ungraded or graded) algebras.