George Mackey

George Whitelaw Mackey (February 1, 1916 – March 15, 2006) was an American mathematician known for his contributions to quantum logic, representation theory, and noncommutative geometry.

Mackey's results were essential tools in the study of the representation theory of nilpotent Lie groups using the method of orbits developed by Alexandre Kirillov in the 1960s.

His notion of "virtual subgroup", introduced in 1966 using the language of groupoids, had a significant influence in ergodic theory.

Another essential ingredient in Mackey's work was the assignment of a Borel structure to the dual object of a locally compact group (specifically a locally compact separable metric group) G. One of Mackey's important conjectures, which was eventually solved by work of James Glimm on C*-algebras, was that G is type I (meaning that all its factor representations are of type I) if and only if the Borel structure of its dual is a standard Borel space.

Lawrence G. Brown, Paul Chernoff, Edward G. Effros, Calvin Moore, Richard Palais, Caroline Series, John Wermer and Robert Zimmer have been doctoral students of Mackey.