The representation category of the quantum group of a non-degenerate bilinear form

2001/11/09 by Julien Bichon, Bichon, Julien
Mathematics · #16W30 #18D10 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.QA #math.RA #msc:16W30 #msc:18D10

paper · pdf · doi:10.48550/arxiv.math/0111114

16 pages

arxiv created 2001/11/09 · openalex publication_date 2001/11/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the representation category of the quantum group of a non-degenerate bilinear form is monoidally equivalent to the representation category of the quantum group SL_q(2), for a well chosen non-zero parameter q. The main ingredient for the proof of this result is the direct and explicit construction of an appropriate Hopf bigalois extension. Then we get, in characteristic zero, a full description of cosemisimple Hopf algebras whose representation semi-ring is isomorphic to the one of SL(2).

Related

• Quantum groups of GL(2) representation type
• Representation theory of a Class of Hopf algebras
• On the classification of Galois objects over the quantum group of a nondegenerate bilinear form
• Module categories over representations of SL_q(2) in the non-semisimple case
• Quantum groups and representations with highest weight