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. ***

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
9503062
Program Officer
Joe W. Jenkins
Project Start
Project End
Budget Start
1995-07-01
Budget End
1997-06-30
Support Year
Fiscal Year
1995
Total Cost
$40,000
Indirect Cost
Name
University of Cincinnati
Department
Type
DUNS #
City
Cincinnati
State
OH
Country
United States
Zip Code
45221