Knot theory with the Lorentz group

S ep 2 00 3 Knot Theory With The Lorentz Group

As pointed out by Buffenoir and Roche in [BR1], the Quantum Lorentz Group has a formal R-matrix and a formal ribbon element. It is possible to describe the action of them in the infinite dimensional quantised representations of the principal series. Given a knot diagram, it is thus possible to make a formal Reshetikin-Turaev evaluation of a numerical knot invariant. After the observation that f...

Quaternions, Lorentz Group and the Dirac Theory

It is shown that a subgroup of SL(2, H), denoted Spin(2, H) in this paper, which is defined by two conditions in addition to unit quaternionic determinant, is locally iso-morphic to the restricted Lorentz group, L ↑ +. On the basis of the Dirac theory using the spinor group Spin(2, H), in which the charge conjugation transformation becomes linear in the quaternionic Dirac spinor, it is shown th...

The 2-generalized Knot Group Determines the Knot

Generalized knot groups Gn(K) were introduced independently by Kelly (1991) and Wada (1992). We prove that G2(K) determines the unoriented knot type and sketch a proof of the same for Gn(K) for n > 2. 1. The 2–generalized knot group Generalized knot groups were introduced independently by Kelly [5] and Wada [10]. Wada arrived at these group invariants of knots by searching for homomorphisms of ...

Knot Theory

Inertiality Implies the Lorentz Group

In his seminal paper of 1905, Einstein derives the Lorentz group as being the coordinate transformations of Special Relativity, under the main assumption that all inertial frames are equivalent. In that paper, Einstein also assumes the coordinate transformations are linear. Since then, other investigators have weakened and varied the linearity assumption. In the present paper, we retain only th...