2003/05/13 by Deepak Parashar, Parashar, Deepak
Mathematics · Physics and Astronomy · #17B37 #81R50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math-ph #math.MP #math.QA #msc:17B37 #msc:81R50
paper · pdf · doi:10.48550/arxiv.math/0305188
4 Pages, Talk given at GROUP24, Paris, July 15-20,2002; to appear in the Proceedings (IoP Conference Series 173)
arxiv created 2003/05/13 · openalex publication_date 2003/05/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the algebro-geometric structure of a novel two-parameter quantum deformation which exhibits the nature of a semidirect or cross-product algebra built upon GL(2) x GL(1), and is related to several other known examples of quantum groups. Following the R-matrix framework, we construct the L+/- functionals and address the problem of duality for this quantum group. This naturally leads to the construction of a bicovariant differential calculus that depends only on one deformation parameter, respects the cross-product structure and has interesting applications. The corresponding Jordanian and hybrid deformation is also explored.