2014/06/27 by H. Bustos, Bustos, H., M. Mantoiu +1
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Primary 47L65 #Secundary 46L55 #math.FA #math.OA #msc:46L55 #msc:47L65
paper · pdf · doi:10.48550/arxiv.1406.7211
22 pages
arxiv created 2014/06/27 · arxiv updated 2014/06/30
We introduce \it covariant structures \(\A,\k),(\a,å),\(\ha,\haa\)\ formed of a separable C^*-algebra \A, a measurable twisted action (\a,å) 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:\G×\hG→\U\M(\A) suitably connected with (\a,å) 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.