Abstract
In this paper, we prove a graded version of Exel’s Effros-Hahn conjecture for Leavitt path algebras. More concretely, we show that any graded primitive ideal of the Leavitt path algebra is the annihilator of a module induced from a graded simple module over an isotropy group algebra. A graded version of Steinberg’s results towards Exel’s conjecture in (B. Steinberg, Ideals of etale ´groupoid algebras and Exel’s Effros-Hahn conjecture, J. Noncommut. Geom., Vol. 15, 2021, pp. 829-839) is also obtained for graded ample groupoid algebras.
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