Meander graphs and Frobenius seaweed Lie algebras. II. (English) Zbl 1394.17022

Coll, Vincent; Hyatt, Matthew; Magnant, Colton; Wang, Hua

J. Gen. Lie Theory Appl. 9, No. 1, Article ID 1000227, 7 p. (2015).

Summary: We provide a recursive classification of meander graphs, showing that each meander is identified by a unique sequence of fundamental graph theoretic moves. This sequence is called the meander’s signature and can be used to construct arbitrarily large sets of meanders, Frobenius or otherwise, of any size and configuration. In certain special cases, the signature is used to produce an explicit formula for the index of seaweed Lie subalgebra of \(\mathfrak{sl}(n)\) in terms of elementary functions.
For Part I see J. Gen. Lie Theory Appl. 5, Article ID G110103, 7 p. (2011; Zbl 1235.17003).

MSC:

17B20

Simple, semisimple, reductive (super)algebras

Keywords:

biparabolic; Frobenius; Lie algebra; meander graphs; seaweed algebra