Graded quasi-Cartan, Cartan, and diagonal pairs correspond exactly to graded twisted Steinberg algebras, and the associated graded discrete twist is unique.
Filtering germs: groupoids associated to inverse semigroups
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On Graded Quasi-Cartan Pairs and Twisted Steinberg Algebras
Graded quasi-Cartan, Cartan, and diagonal pairs correspond exactly to graded twisted Steinberg algebras, and the associated graded discrete twist is unique.