Zeitschrift für verallgemeinerte Lügentheorie und -anwendungen

Meander Graphs and Frobenius Seaweed Lie Algebras III

Abstract

Vincent Coll, Dougherty A, Hyatt M and Mayers N

We investigate properties of a Type-A meander, here considered to be a certain planar graph associated to seaweed subalgebra of the special linear Lie algebra. Meanders are designed in such a way that the index of the seaweed may be computed by counting the number and type of connected components of the meander. Specifically, the simplicial homotopy types of Type-A meanders are determined in the cases where there exist linear greatest common divisor index formulas for the associate seaweed. For Type-A seaweeds, the homotopy type of the algebra, defined as the homotopy type of its associated meander, is recognized as a conjugation invariant which is more granular than the Lie algebra's index.