\(C^*\)-algebraic covariant structures

zbMATH Open1377.47024arXiv1406.7211MaRDI QIDQ2834134

Marius Măntoiu, H. Bustos

Publication date: 25 November 2016

Published in: Houston Journal of Mathematics (Search for Journal in Brave)

Abstract: We introduce {it covariant structures} $left(A,k),(a,aa),(ha,haa)ight$ formed of a separable $C^{*}$-algebra $A$, a measurable twisted action $(a,aa)$ of the second-countable locally compact group $G$,, a measurable twisted action $(ha,haa)$ of another second-countable locally compact group $hG$ and a strictly continuous function $k:GimeshGoUM(A)$ suitably connected with $(a,aa)$ and $(ha,haa)$,. Natural notions of covariant morphisms and representations are considered, leading to a sort of twisted crossed product construction. Various $C^{*}$-algebras emerge by a procedure that can be iterated indefinitely and that also yields new pairs of twisted actions. Some of these $C^{*}$-algebras are shown to be isomorphic. The constructions are non-commutative, but are motivated by Abelian Takai duality that they eventually generalize.

Full work available at URL: https://arxiv.org/abs/1406.7211

zbMATH Keywords

\(C^*\)-algebradynamical systemcrossed productTakai dualitygroup cocycle

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55) Crossed product algebras (analytic crossed products) (47L65)

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