R matrix and bicovariant calculus for the inhomogeneous quantum groups IGLq(n)

1992/11/05 by Leonardo Castellani · 10 citations
Chemistry · Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Chemistry #Combinatorics #Differential calculus #Group (periodic table) #Homogeneous #Mathematics #Matrix (chemical analysis) #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum #Quantum group #Quantum mechanics #R-matrix #hep-th

paper · pdf · doi:10.1016/0370-2693(93)91829-c

published in Physics Letters B 298(3-4), 335-338 (Elsevier BV) · 8 pp., LaTeX, DFTT-59/92

arxiv created 1992/11/05 · openalex publication_date 1993/01/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We find the R matrix for the inhomogeneous quantum groups whose homogeneous part is GL_q(n), or its restrictions to SL_q(n),U_q(n) and SU_q(n). The quantum Yang-Baxter equation for R holds because of the Hecke relation for the braiding matrix of the homogeneous subgroup. A bicovariant differential calculus on IGL_q(n) is constructed, and its application to the D=4 Poincaré group ISL_q(2,\Cb) is discussed.

Citations

• Differential calculus on compact matrix pseudogroups (quantum groups)
• AN INTRODUCTION TO NONCOMMUTATIVE DIFFERENTIAL GEOMETRY ON QUANTUM GROUPS