The equation [B,(A-1)(A,B)] = 0 and virtual knots and links

• Autorzy: Stephen Budden , Roger Fenn
• Języki publikacji: EN

Abstrakty

EN

Let A, B be invertible, non-commuting elements of a ring R. Suppose that A-1 is also invertible and that the equation [B,(A-1)(A,B)] = 0 called the fundamental equation is satisfied. Then this defines a representation of the algebra ℱ = A, B | [B,(A-1)(A,B)] = 0. An invariant R-module can then be defined for any diagram of a (virtual) knot or link. This halves the number of previously known relations and allows us to give a complete solution in the case when R is the quaternions.

Kategorie tematyczne

• 57M27: Invariants of knots and 3-manifolds
• 57M25: Knots and links in S 3

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2004
• Tom: 184
• Numer: 1
• Strony: 19-29

Daty

wydano

2004

Twórcy

autor

Stephen Budden

• School of Mathematical Sciences, University of Sussex, Falmer, Brighton, BN1 9RH, England

autor

Roger Fenn

• School of Mathematical Sciences, University of Sussex, Falmer, Brighton, BN1 9RH, England

Identyfikatory

DOI

10.4064/fm184-0-2