Mathematical Sciences: Endomorphisms of von Nuemann Algebras

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9401464 Powers Powers proposes to study continuous one parameter semigroups of star endomorphisms of operator algebras. Particular emphasis will be given to the simplest case of the full algebra of operators on Hilbert space and binary shifts on hyperfinite factors of type II_1. Pimsner will continue the investigation of Kasparov's bivariant K-functor in its equivariant form, especially in its applications to the study of C*-algebras and groups and their actions on different kinds of spaces. Investigations will also be made of the related study of Hilbert bimodules and their connection to both KK-theory and to the theory of subfactors. Operators can be considered as infinite generalizations of matrices. Given their natural addition and multiplication, a collection of operators can be considered as an operator algebra. A subalgebra of certain types of operator algebras is called a subfactor. The relations between subfactors has remarkable connection with geometry and mathematical physics. The work of Pimsner will contribute to the connections. Powers will study actions on operator algebras. These actions are related to important questions in the theory of subfactors mentioned above. ***