Mathematical Sciences: Endomorphisms of von Neumann Algebras

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Professors Powers and Pimsner will study aspects of the theory of C*-algebras and von Neumann algebras. Professor Powers' work will concern continuous one parameter semigroups of *-endomorphisms of C*-algebras and von Neumann algebras with particular emphasis on the von Neumann algebra of all bounded operators on a Hilbert space. Professor Pimsner will study the K-theory of operator algebras, especially that of group C*-algebras of crossed products by certain classes of groups. The notion of a C* algebra is an abstraction of the idea of a family of linear transformations on a space. These transformations can also be thought of as having values in the states of the space, and the property of this family which is responsible for the symbol * is that the algebra is generated by transformations whose values in these states are real numbers. The fact that these objects appear naturally in many branches of mathematics and physics makes them important to study.