Mathematical Sciences: Endomorphisms of von Nuemann Algebras

小行星9401464 Powers提出研究算子代数的星星自同态的连续单参数半群。特别强调将给予最简单的情况下，全代数的运营商在希尔伯特空间和二元移位超有限因素的类型II_1。皮姆斯纳将继续调查卡斯帕罗夫的双变K-函子在其等变形式，特别是在其应用研究的C*-代数和群体及其行动的不同种类的空间。 调查也将作出相关的研究希尔伯特双模和他们的联系都KK理论和理论的子因子。 算子可以看作是矩阵的无限推广。给定它们的自然加法和乘法，一个运算符的集合可以被认为是一个运算符代数。某些类型的算子代数的子代数称为子因子。子因子之间的关系与几何和数学物理有着密切的联系。Pimsner的工作将有助于建立联系。权力将研究行动的运营商代数。这些行为与上述子因素理论中的重要问题有关。 ***

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. ***