Leírás
In a joint work with Ruy Exel and Héctor Pinedo, given a field K and an ample (not necessarily Hausdorff) groupoid G, we define the concept of a line
bundle over G inspired by the well known notion from the theory of C*-algebras. If E is such a line bundle, we construct the associated twisted Steinberg algebra in terms of sections of E, extending the original construction introduced independently by Steinberg, and by Clark, Farthing, Sims and Tomforde. We also generalize the recent construction of
(cocycle) twisted Steinberg algebras of Armstrong, Clark, Courtney, Lin, Mccormick and Ramagge. We then extend
Steinberg's theory of induction of modules, not only to the twisted case, but to the much more general case of
regular inclusions of algebras. Among our main results, we show that, under appropriate conditions, every irreducible module is induced by an irreducible module over a certain abstractly defined isotropy algebra. We also describe a process of disintegration of modules and use it to prove a version of the Effros-Hahn conjecture, showing that every primitive ideal coincides with the annihilator of a module induced from isotropy.
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