The Representation Category of the Quantum Group of a Non-degenerate Bilinear Form

By Julien Bichon. 2001

122 citations recorded by the source corpus.

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 key ingredient for the proof of this result is the direct and explicit construction of an appropriate Hopf bigalois extension. Then we get, when the base field is of characteristic zero, a full description of cosemisimple Hopf algebras whose representation semi-ring is isomorphic to the one of SL(2).

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/45f5e2603f879de0929dde397ff85eafadce489a

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In Algebra and Number Theory

1. Julien Bichon
2. Pavel Etingof
3. V. Ostrik
4. Michael Brannan
5. Benoît Collins
6. Roland Vergnioux
7. An De Rijdt
8. S. Vaes

In Geometry and Topology

1. Michael Brannan
2. Julien Bichon
3. Pavel Etingof
4. Roland Vergnioux
5. V. Ostrik
6. T. Banica
7. Benoît Collins
8. Amaury Freslon

In Mathematical Physics

1. Michael Brannan
2. Julien Bichon
3. Roland Vergnioux
4. Pavel Etingof
5. Benoît Collins
6. T. Banica
7. V. Ostrik
8. Amaury Freslon

Citations in the corpus

• The Connes embedding property for quantum group von Neumann algebras (2014, background): “is paper. These quantum groups were first introduced in the operator algebra ic framework by Wang [42]. Purely algebraic versions of these objects were also introduced by Dubois-Violette and Launer in [21]. Let N ≥ 2. The free orthogonal quantum group O+ N is the compact quantum group given (in unive”
• Module categories over representations of $SL_q(2)$ and graphs (2003, background): “. We see from Theorem 2.5 that the fiber functors on C q are classified by a vector space V and a bilinear form E : V ⊗V → C such that Tr(E(Et)−1) = −q−q−1. This is exactly the result of J. Bichon, see [Bi] who classified all Hopf algebras H such that the category of comodules over H is tensor equivale”
• Ergodic Coactions with Large Multiplicity and Monoidal Equivalence of Quantum Groups (2005, background): “6 in [6] and the results in [7] yields an alternative proof for the fact that Ao(F1, F2) 6= 0.”