Realizing corners of Leavitt path algebras as Steinberg algebras, with corresponding connections to graph C⁎-algebras

We show that the endomorphism ring of any nonzero finitely generated projective module over Leavitt path algebra LK(E) an arbitrary graph E with coefficients in a field K is isomorphic to Steinberg algebra. This yields particular every corner its turn gives K-algebra local units which Morita equivalent row-countable Moreover, we prove by projection C⁎-algebra countable ample groupoid.