Classification of the GL(3) Quantum Matrix Groups

Details Classification of the GL(3) Quantum Matrix Groups Classification of the GL(3) Quantum Matrix Groups

1994-12-21

arxiv.org/abs/q-alg/9412009v1

Physics

High Energy Physics

High Energy Physics - Theory

28 pages, Latex

Scientific paper

We define quantum matrix groups GL(3) by their coaction on appropriate quantum planes and the requirement that the Poincare series coincides with the classical one. It is shown that this implies the existence of a Yang-Baxter operator. Exploiting stronger equations arising at degree four of the algebra, we classify all quantum matrix groups GL(3). We find 26 classes of solutions, two of which do not admit a normal ordering. The corresponding R-matrices are given.

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