18 citations · 103 across the 34 of their papers we have counts for
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Noncommutative Pierce Duality between Steinberg Rings and Ample Ringoid Bundles
Tristan Bice
Classic work of Pierce and Dauns-Hofmann shows that biregular rings are dual to simple ring bundles over Stone spaces. We extend this duality to Steinberg rings, a purely algebraic…
Representing Structured Semigroups on Etale Groupoid Bundles
Tristan Bice
We examine a semigroup analogue of the Kumjian-Renault representation of C*-algebras with Cartan subalgebras on twisted groupoids. Specifically, we show how to represent semigroups…
Lattice-Free and Point-Free: Vickers Duality for Subbases of Stably Locally Compact Spaces
Tristan Bice, Wieslaw Kubis
Inspired by classic work of Wallman and more recent work of Jung-Kegelmann-Moshier and Vickers, we show how to encode general subbases of stably locally compact spaces via certain…
Wallman Duality for Semilattice Subbases
Tristan Bice, Wiesław Kubiś
We extend Wallman's classic duality from lattice bases to semilattice subbases and from compact to locally closed compact spaces. Moreover, we make this duality functorial via appr…
Reconstructing Etale Groupoids from Semigroups
Tristan Bice, Lisa Orloff Clark
We unify various étale groupoid reconstruction theorems such as: 1) Kumjian-Renault's reconstruction from a groupoid C*-algebra. 2) Exel's reconstruction from an ample inverse semi…