NSF Org:	DMS Division Of Mathematical Sciences
Recipient:	UNIVERSITY OF PUERTO RICO
Initial Amendment Date:	May 21, 1999
Latest Amendment Date:	May 25, 2001
Award Number:	9970840
Award Instrument:	Continuing Grant
Program Manager:	Joe W. Jenkins DMS  Division Of Mathematical Sciences MPS  Directorate for Mathematical and Physical Sciences
Start Date:	June 1, 1999
End Date:	May 31, 2003 (Estimated)
Total Intended Award Amount:	$130,551.00
Total Awarded Amount to Date:	$130,551.00
Funds Obligated to Date:	FY 1999 = $43,517.00 FY 2000 = $43,517.00 FY 2001 = $43,517.00
History of Investigator:	Guihua Gong (Principal Investigator) ghgong@gmail.com Liangqing Li (Co-Principal Investigator)
Recipient Sponsored Research Office:	University of Puerto Rico-Rio Piedras 39 PONCE DE LEON AVE SAN JUAN PR  US  00931 (787)763-4949
Sponsor Congressional District:	00
Primary Place of Performance:	University of Puerto Rico-Rio Piedras 39 PONCE DE LEON AVE SAN JUAN PR  US  00931
Primary Place of Performance Congressional District:	00
Unique Entity Identifier (UEI):	Q3LLLDFHPNL3
Parent UEI:
NSF Program(s):	ANALYSIS PROGRAM
Primary Program Source:	app-0100  01000102DB NSF RESEARCH & RELATED ACTIVIT app-0199
Program Reference Code(s):	OTHR, 0000
Program Element Code(s):	128100
Award Agency Code:	4900
Fund Agency Code:	4900
Assistance Listing Number(s):	47.049

ABSTRACT

Abstract
Gong/Li

Simple C*-algebras are basic building blocks in the theory of C*-algebras. The principal investigators, Guihua Gong and Liangqing Li, propose to continue their research on the classification of simple, separable, amenable C*-algebras. They also plan to apply the classification results and the techniques developed in the classification project to study group actions on C*-algebras and differential topology (e.g. the Novikov conjecture on the homotopy invariance of higher signature).

The passage from a finite to an infinite number of degrees of freedom in quantum physics led to the mathematical theory of certain infinite dimensional algebras, called C*-algebras. A C*-algebra is an algebraic system, similar to that of numbers, with its operations of addition, subtraction, multiplication, and division. But unlike the multiplication for numbers, the multiplication in a C*-algebra is not commutative ---- that is, in general, X times Y is not as same as Y times X. This important feature corresponds to Heisenberg uncertainty principle in Quantum Mechanics. The simple C*-algebras are those that cannot be broken into smaller pieces, and in some sense all C*-algebras are built out of them. The investigators propose to work on a complete enumeration (or classification) of simple amenable C*-algebras. They expect that progress on the proposed research will result in important contributions to several mathematical fields including operator algebras, differential topology, and also to the understanding of the infinite dimensional world of quantum physics.

Please report errors in award information by writing to: awardsearch@nsf.gov.