Mathematical Sciences: Trace Extensions and Commutator Spaces with Applications to the Homology, Determinants and K-Theory of Operator Ideals

小行星9503062韦斯 这个项目的一个主要目标是确定Hochschild和循环上同调群的有界希尔伯特空间算子相对于任意的2-边理想的全代数。这些计算最近被联系到表征交换子理想。迹扩展和结构的recruitors和换向器空间将被调查和利用，以产生信息的同源性，决定因素和K-理论的经营者理想。 这个项目处于两个数学领域的交界处。一方面，该项目涉及精细的显式计算的算子。算子理论是作为数学物理方程的抽象而发展起来的。交换子对应于有序观测之间的差。在另一个方向上，一个操作符的集合通常可以被认为是一个代数结构，称为操作符代数。这类代数的某些不变量在数学、物理和几何等学科中起着重要的作用。这个项目的目的是实现这些不变量通过执行微妙的换向器计算。 ***

9503062 Weiss A principal goal of this project is to determine the Hochschild and cyclic cohomology groups for the full algebra of bounded Hilbert space operators relative to an arbitrary 2-sided ideal. These computations have been recently linked to characterizing commutator ideals. Trace extensions and the structure of commutators and commutator spaces will be investigated and exploited to yield information on the homology, determinants and K-theory of operator ideals. This project lies at the interface of two mathematical areas. On one side, the project concerns delicate explicit computations of commutators of operators. Operator theory evolved as an abstraction of the equations of mathematical physics. A commutator corresponds to the difference between ordered observations. In another direction, a collection of operators can often be considered as an algebraic structure called an operator algebra. Certain invariants of such algebras play an important role in several disciplines including mathematical physics and geometry. The purpose of this project is to realize these invariants by performing delicate commutator computations. ***