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Dieck T. Quantum Groups and Knot Algebra

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Dieck T. Quantum Groups and Knot Algebra
Tammo tom Dieck, 2000. — 201 p.
Tensor categories
Categories
Functors
Adjoint functors
Tensor categories
The neutral object
Tensor functors
Braided categories
The Yang-Baxter relation. Twist
Universal braid categories
Pairings and copairings
Duality
Duality and braiding
Ribbon categories
Tensor module categories
Categories with cylinder braiding
Rooted structures
Hopf Algebras
Hopf algebras
Modules and Comodules
Dual modules
The finite dual
Pairings
The quantum double
Yetter-Drinfeld modules
Braiding
Quantum double and R-matrix
Duality and braiding
Cobraiding
The FRT-construction
Cylinder braiding
Cylinder forms
Tensor representations of braid groups
Cylinder forms from four braid pairs
The four braid relation and R-matrices
The Quantum Group SL2
The Hopf algebra U
Integrable U-modules
The algebra B and its pairing
The algebra U as a quantum double
The R-matrix for U
The quantum Weyl group
The cylinder braiding for U-modules
The universal cylinder twist
Binomial coefficients
Knot algebra
Braid groups, Coxeter groups, and related algebras
Braid groups of type B
Braids of type B
Categories of bridges
Representations of bridge categories
General categories of bridges
Representations of Hecke algebras
Temperley-Lieb algebras
Birman-Wenzl-Murakami algebras of type B
Tensor representations of braid groups
The universal twist
Cylinder forms
Cylinder twist
Cylinder forms from four braid pairs
The example sl2
The cylinder braiding for U-modules
The universal cylinder twist
The structure of the cylinder twist
The cylinder twist on irreducible modules
Categories of ribbons
Skein relations
A representation of rooted cylinder ribbons
The Kauffman functor
Categories of bridges
Symmetric bridges
Presentation of the categories
An algebraic model for TB
The category of coloured cylinder ribbons
Trivalent graphs
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