Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Monoidal and Braided Categories
- 2 Algebras and Coalgebras in Monoidal Categories
- 3 Quasi-bialgebras and Quasi-Hopf Algebras
- 4 Module (Co)Algebras and (Bi)Comodule Algebras
- 5 Crossed Products
- 6 Quasi-Hopf Bimodule Categories
- 7 Finite-Dimensional Quasi-Hopf Algebras
- 8 Yetter–Drinfeld Module Categories
- 9 Two-sided Two-cosided Hopf Modules
- 10 Quasitriangular Quasi-Hopf Algebras
- 11 Factorizable Quasi-Hopf Algebras
- 12 The Quantum Dimension and Involutory Quasi-Hopf Algebras
- 13 Ribbon Quasi-Hopf Algebras
- Bibliography
- Index
10 - Quasitriangular Quasi-Hopf Algebras
Published online by Cambridge University Press: 21 February 2019
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Monoidal and Braided Categories
- 2 Algebras and Coalgebras in Monoidal Categories
- 3 Quasi-bialgebras and Quasi-Hopf Algebras
- 4 Module (Co)Algebras and (Bi)Comodule Algebras
- 5 Crossed Products
- 6 Quasi-Hopf Bimodule Categories
- 7 Finite-Dimensional Quasi-Hopf Algebras
- 8 Yetter–Drinfeld Module Categories
- 9 Two-sided Two-cosided Hopf Modules
- 10 Quasitriangular Quasi-Hopf Algebras
- 11 Factorizable Quasi-Hopf Algebras
- 12 The Quantum Dimension and Involutory Quasi-Hopf Algebras
- 13 Ribbon Quasi-Hopf Algebras
- Bibliography
- Index
Summary
By using categorical tools, we introduce the concept of quasitriangular (QT) quasi-bialgebras. For QT quasi-Hopf algebras we show that the square of the antipode is an inner automorphism, and therefore bijective. We uncover the QT structure of the quantum double D(H) of a finite-dimensional quasi-Hopf algebra H, and characterize D(H) as a biproduct quasi-Hopf algebra in the case when H itself is QT.
- Type
- Chapter
- Information
- Quasi-Hopf AlgebrasA Categorical Approach, pp. 381 - 406Publisher: Cambridge University PressPrint publication year: 2019