NATURALITY OF SYMMETRIC IMPRIMITIVITY THEOREMS

作者：An Huef Astrid^*; Kaliszewski S; Raeburn Iain; Williams Dana P

来源：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2013, 141(7): 2319-2327.

DOI：10.1090/S0002-9939-2013-11712-0

• Symmetric imprimitivity theorem
• proper actions on C*-algebras
• naturality
• fixed-point algebras
• crossed products

The first imprimitivity theorems identified the representations of groups or dynamical systems which are induced from representations of a subgroup. Symmetric imprimitivity theorems identify pairs of crossed products by different groups which are Morita equivalent and hence have the same representation theory. Here we consider commuting actions of groups H and K on a C*-algebra which are saturated and proper as defined by Rieffel in 1990. Our main result says that the resulting Morita equivalence of crossed products is natural in the sense that it is compatible with homomorphisms and induction processes.

• 出版日期2013-7