vix.ing · top · new · best · stats · spec

Classification of the GL(3) Quantum Matrix Groups

1994/12/21 by Holger Ewen, Ewen, Holger, O. Ogievetsky +2
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #hep-th #math.QA #q-alg

paper · pdf · doi:10.48550/arxiv.q-alg/9412009

28 pages, Latex

arxiv created 1994/12/21 · openalex publication_date 1994/12/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related