ORIENTED QUANTUM ALGEBRAS, CATEGORIES AND INVARIANTS OF KNOTS AND LINKS

DOI10.1142/S0218216501001268zbMath1008.57010arXivmath/0006019OpenAlexW2057789408MaRDI QIDQ4541062

Louis H. Kauffman, David E. Radford

Publication date: 30 July 2002

Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0006019

zbMATH Keywords

quantum invariantsHOMFLYknot invariantoriented quantum algebra

Mathematics Subject Classification ID

Related Items (13)

Quantum algebras, quantum coalgebras, invariants of 1-1 tangles and knots ⋮ Rotational virtual knots and quantum link invariants ⋮ Bottom tangles and universal invariants ⋮ On the universal \(sl_{2}\) invariant of boundary bottom tangles ⋮ On oriented quantum algebras derived from representations of the quantum double of a finite-dimensional Hopf algebra. ⋮ ON THE TENSOR PRODUCT OF AN ORIENTED QUANTUM ALGEBRA WITH ITSELF ⋮ A Method to Construct Oriented Quantum Algebras ⋮ Modified graded Hennings invariants from unrolled quantum groups and modified integral ⋮ On the universal sl₂ invariant of Brunnian bottom tangles ⋮ A unified Witten-Reshetikhin-Turaev invariant for integral homology spheres ⋮ Trace-like functionals on the double of the Taft Hopf algebra. ⋮ Oriented quantum algebras and invariants of knots and links ⋮ A Hennings type invariant of 3-manifolds from a topological Hopf superalgebra

Cites Work

• On knot invariants related to some statistical mechanical models
• State models and the Jones polynomial
• The Yang-Baxter equation and invariants of links
• Quantum algebra structures on \(n\times n\) matrices
• Ribbon graphs and their invariants derived from quantum groups
• On a parameterized family of twist quantum coalgebras and the bracket polynomial
• Minimal quasitriangular Hopf algebras
• Centrality and the KRH Invariant
• GAUSS CODES, QUANTUM GROUPS AND RIBBON HOPF ALGEBRAS
• Invariants of Links and 3-Manifolds Obtained from Hopf Algebras
• INVARIANTS OF 3-MANIFOLDS DERIVED FROM FINITE DIMENSIONAL HOPF ALGEBRAS

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