FROM TWISTED INVERSE SEMIGROUPS TO TWISTED SELF-SIMILAR ACTIONS AND THEIR C*-ALGEBRAS

Prelegent(ci)

BARTOSZ K. KWAŚNIEWSKI

Afiliacja

Uniwersytet w Białymstoku, Poland

Język referatu

angielski

Termin

28 października 2026 17:15

Informacje na temat wydarzenia

IMPAN 405 & ZOOM

Tytuł w języku polskim

FROM TWISTED INVERSE SEMIGROUPS TO TWISTED SELF-SIMILAR ACTIONS AND THEIR C*-ALGEBRAS

Seminarium

North Atlantic Noncommutative Geometry Seminar

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We first consider general twisted inverse semigroups and explain how to associate twisted ample groupoids to them, together with their universal, reduced, and essential C*-algebras. We discuss general criteria for these algebras, including uniqueness theorems and conditions for simplicity and pure infiniteness. Next, we introduce twisted self-similar actions of discrete groupoids on arbitrary directed graphs and define the associated twisted Toeplitz and Cuntz-Krieger algebras, along with their reduced and essential versions. This significantly extends the class of actions and C*-algebras considered by Nekrashevich,  Exel and Pardo, Laca and Raeburn and Ramagge and Whittaker, and others. The twisted inverse semigroup model allows us to establish uniqueness theorems for these algebras and characterise them when their canonical diagonal subalgebras are Cartan. We also give conditions ensuring that the essential Cuntz-Krieger algebra is simple and purely infinite. A complementary approach based on C*-correspondences yields connections between the amenability of the acting groupoid and the nuclearity of the associated Toeplitz algebra, as well as criteria for the full, reduced, and essential C*-algebras to coincide. Finally, time permitting, I will explain how these constructions, together with most of the results, extend to the more general setting of L^p-operator algebras. (Based on joint work with Alex Mundey.)

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