Home : Book details : Book description

Description of  Crossed Products by Hecke Pairs (Memoirs of the American Mathematical Society)

The author develops a theory of crossed products by actions of Hecke pairs $(G, Gamma )$, motivated by applications in non-abelian $C*$-duality. His 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. The author starts by laying the $*$-algebraic foundations of these crossed products by Hecke pairs and exploring their representation theory and then proceeds to study their different $C*$-completions. He establishes that his construction coincides with that of Laca, Larsen and Neshveyev whenever they are both definable and, as an application of his theory, he proves a Stone-von Neumann theorem for Hecke pairs which encompasses the work of an Huef, Kaliszewski and Raeburn. Read more