Mathematical Sciences: RUI: Krein Space Representations and Index Theory for Derivations

Price教授将讨论与自同态半群的指标理论有关的算子代数理论中的一些问题。在这项工作中，Price教授将继续他与Jorgensen的工作，他们将Arveson-Powers指标推广到一个集合，该集合为算子代数上的某些导数分配了一个指标。他希望继续与鲍尔斯一起研究一个相关问题，即分析对称无界算子的第二次量子化的产生器扩展。他也将研究一类算子代数的同构不变量，这类算子代数的结构类似于单参数的孔兹代数族。最后Price将继续他的项目，让本科生熟悉一些涉及算子代数的研究课题。Price教授的课题涉及自伴随算子代数。这些对象由希尔伯特空间算子族（无限复数矩阵）组成，它们有一个有趣的性质：代数是由代数上任何状态的值都是实数的算子生成的。这种性质使得这些代数对物理学很重要，事实上，物理学是研究它们的最初动机。

Professor Price will consider some questions in the theory of operator algebras related to the index theory for semigroups of endomorphisms. In this work Professor Price will continue his work with Jorgensen on their extension of the Arveson-Powers index to a setting which assigns an index to certain derivations on operator algebras. He expects to continue his work with Powers on a related problem of analyzing the generator extensions of the second quantization of a symmetric unbounded operator. He also will study isomorphism invariants for a class of operator algebras whose structure resembles that of a one parameter family of Cuntz algebras. Finally Price will continue his project of acquainting undergraduates with certain research topics involving operator algebras. Professor Price's project involves self-adjoint operator algebras. These objects consist of families of Hilbert space operators (infinite matrices of complex numbers) which have an interesting property: the algebra is generated by operators whose value in any state on the algebra is a real number. This property makes these algebras important for physics and indeed physics was the original motivation for their study.