Crossed products by Hecke pairs I: *-algebraic theory

Abstract

We develop a theory of crossed products by "actions" of Hecke pairs $(G,\Gamma )$, motivated by applications in non-abelian $C^{\ast }$-duality. Our approach gives back the usual crossed product construction whenever $G/\Gamma$ is a group and retains many of the aspects of crossed products by groups. In this first of two articles we lay the ${}^{\ast }$-algebraic foundations of these crossed products by Hecke pairs and we explore their representation theory.

76 pages

References in corpus (1)

• From Physics to Number Theory via Noncommutative Geometry. Part I: Quantum Statistical Mechanics of Q-lattices

Cited by in corpus (1)

• Crossed-products by locally compact groups: Intermediate subfactors