Quantum Matrix Pairs

Details Quantum Matrix Pairs Quantum Matrix Pairs

1999-11-02

arxiv.org/abs/math/9911015v2

Lett.Math.Phys. 52 (2000) 277-290

Mathematics

Quantum Algebra

14 pages, no figures, Latex. Revised version (June 2000) to appear in Lett. Math. Phys

Scientific paper

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.

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