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Ideals of etale groupoid algebras and Exel's Effros-Hahn conjecture. (arXiv:1810.10580v1 [math.RA])
来源于:arXiv
We extend to arbitrary commutative base rings a recent result of Demeneghi
that every ideal of an ample groupoid algebra over a field is an intersection
of kernels of induced representations from isotropy groups, with a much shorter
proof, by using the author's Disintegration Theorem for groupoid
representations. We also prove that every primitive ideal is the kernel of an
induced representation from an isotropy group; however, we are unable to show,
in general, that it is the kernel of an irreducible induced representation. If
each isotropy group is finite (e.g., if the groupoid is principal) and if the
base ring is Artinian (e.g., a field), then we can show that every primitive
ideal is the kernel of an irreducible representation induced from isotropy. 查看全文>>