4 papers
Bi-oriented Quantum Algebras, and a Generalized Alexander Polynomial for Virtual Links
Louis H. Kauffman, David E. Radford
This paper discusses the construction of a generalized Alexander polynomial for virtual knots and links, and the reformulation of this invariant as a quantum link invariant. The al…
Oriented Quantum Algebras and Invariants of Knots and Links
Louis H. Kauffman, David E. Radford
In GT/0006019 oriented quantum algebras were motivated and introduced in a natural categorical setting. Invariants of knots and links can be computed from oriented quantum algebras…
Oriented Quantum Algebras, Categories and Invariants of Knots and Links
Louis H. Kauffman, David E. Radford
This paper defines the concept of an oriented quantum algebra and develops its application to the construction of quantum link invariants. We show that all known quantum link invar…
On Two Proofs for the Existence and Uniqueness of Integrals for Finite-Dimensional Hopf Algebras
Louis H. Kauffman, David E. Radford
This paper has two purposes. The first is to explicate the diagrammatic approach to Hopf algebras due to Kuperberg, and to examine his proof of the existence and uniqueness of inte…