Classification of the GL(3) Quantum Matrix Groups

Holger Ewen , Oleg Ogievetsky (1, 2)

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332

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.

Domaines: Algèbres quantiques [math.QA]; Physique des Hautes Energies - Théorie [hep-th]

Holger Ewen, Oleg Ogievetsky. Classification of the GL(3) Quantum Matrix Groups. 1994. ⟨hal-00473314⟩