Graded quantum groups

2003/12/17 by Alexis Virelizier, Virelizier, Alexis
Mathematics · #17B37 #81R50 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:17B37 #msc:81R50

paper · pdf · doi:10.48550/arxiv.math/0312330

18 pages

arxiv created 2003/12/17 · openalex publication_date 2003/12/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Starting from a Hopf algebra endowed with an action of a group G by Hopf automorphisms, we construct (by a twisted double method) a quasitriangular Hopf G-coalgebra. This method allows us to obtain non-trivial examples of quasitriangular Hopf G-coalgebras for any finite group G and for infinite groups G such as GL(n,K). In particular, we define the graded quantum groups.

Related

• The Coalgebra Automorphism Group of Hopf Algebra k_q[x, x^-1, y]
• Quasitriangular (G-cograded) multiplier Hopf algebras
• Quasitriangular and differential structures on bicrossproduct Hopf algebras
• Hopf group-coalgebras
• Finite-dimensional quasi-Hopf algebras of Cartan type