IJPAM: Volume 40, No. 4 (2007)

THE GEOMETRY OF QUANTUM PRINCIPAL
BUNDLE COHERENT ALGEBRA SHEAVES

Stanley M. Einstein-Matthews$^1$, Molobe Mohlala$^2$
$^{1,2}$Department of Mathematics
Howard University
2441, 6-th. Street N.W.
Washington D.C., 20059, USA
$^1$e-mail: seinstein-math@howard.edu
$^2$e-mail: m_mohlala@howard.edu


Abstract.In this article, the main purpose is to continue the construction, using sheaf theory, of quantum principal bundle algebras sheaves started by Markus J. Pflaum in [#!mPf94!#]. We generalize his construction to higher order differential calculi and extend this further to obtain quantum principal bundle coherent algebra sheaves (see definition below). The main results of our study include the construction of quantum connections, quantum curvatures, quantum Chern-Weil homomorphism and quantum characteristic classes for the quantum principal bundle coherent algebra sheaves.

Received: September 27, 2007

AMS Subject Classification: 53C05, 57R20, 57R22, 58B32, 58B34, 20G42, 46L87, 81R50, 81R60

Key Words and Phrases: quantum coherent algebra sheaf, Hopf algebra, quantum space, quantum principal bundle coherent algebra sheaves, quantum connections, quantum curvatures, quantum Chern-Weil homomorphism, quantum characteristic classes

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 40
Issue: 4