DUALITY, CROSSING AND MACLANES COHERENCE Academic Article uri icon

abstract

  • §1. Introduction In a recent series of papers [ 1-5] on rational conformal field theories in two dimensions, certain constraints were introduced on matrices, the knowledge of which determines the theory. These constraints are associated with certain transformations of graphs. An examination of their form shows that they are similar to constraints introduced by MacLane [6] many years ago in category theory. In the present article we explain the nature of these constraints and their relation to MacLane's theory. This will then allow us to apply MacLane's results (in a recently extended form [ 16], [ 17]) to determine a generating set for these constraints. The content of this paper was obtained in the mathematical physics seminar at Tel Aviv University in June and the early part of July of 1988 and circulated in preprint form at that time. It was presented in a slightly revised form at the conference on Hopf algebras at the University of Beersheba in early …

publication date

  • January 1, 1990