Some Remarks on the Quantum Double

Abstract

We recall the abstract theory of Hopf algebra bicrossproducts and double cross products due to the author. We use it to develop some less-well known results about the quantum double as a twisting, as an extension and as $q$-Lorentz group.

15 pages

References in corpus (6)

• Quantum group gauge theory on quantum spaces
• Braided Momentum Structure of the q-Poincare Group
• Quantum and Braided Linear Algebra
• Free Braided Differential Calculus, Braided Binomial Theorem and the Braided Exponential Map
• q-Euclidean space and quantum group wick rotation by twisting
• Braided Matrix Structure of the Sklyanin Algebra and of the Quantum Lorentz Group

Cited by in corpus (6)

• Deformed and extended Galilei group Hopf algebras
• On weak Hopf symmetry and weak Hopf quantum double model
• Weak Hopf non-invertible symmetry-protected topological spin liquid and lattice realization of (1+1)D symmetry topological field theory
• Twisting cocycles in fundamental representation and triangular bicrossproduct Hopf algebras
• 2-Drinfel'd double symmetry of the 4d Kitaev model
• The restricted quantum double of the Yangian