Quantum Matrix Pairs
Quantum Algebra
2007-05-23 v2 General Relativity and Quantum Cosmology
High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
The notion of quantum matrix pairs is defined. These are pairs of matrices with non-commuting entries, which have the same pattern of internal relations, q-commute with each other under matrix multiplication, and are such that products of powers of the matrices obey the same pattern of internal relations as the original pair. Such matrices appear in an approach by the authors to quantizing gravity in 2 space and 1 time dimensions with negative cosmological constant on the torus. Explicit examples and transformations which generate new pairs from a given pair are presented.
Cite
@article{arxiv.math/9911015,
title = {Quantum Matrix Pairs},
author = {J. E. Nelson and R. F. Picken},
journal= {arXiv preprint arXiv:math/9911015},
year = {2007}
}
Comments
14 pages, no figures, Latex. Revised version (June 2000) to appear in Lett. Math. Phys