Multi-Colour Braid-Monoid Algebras

Details Multi-Colour Braid-Monoid Algebras Multi-Colour Braid-Monoid Algebras

1993-03-30

arxiv.org/abs/hep-th/9303161v1

J.Phys. A26 (1993) 7435-7460

Physics

High Energy Physics

High Energy Physics - Theory

32 pages

Scientific paper

10.1088/0305-4470/26/24/018

We define multi-colour generalizations of braid-monoid algebras and present explicit matrix representations which are related to two-dimensional exactly solvable lattice models of statistical mechanics. In particular, we show that the two-colour braid-monoid algebra describes the Yang-Baxter algebra of the critical dilute A-D-E models which were recently introduced by Warnaar, Nienhuis, and Seaton as well as by Roche. These and other solvable models related to dense and dilute loop models are discussed in detail and it is shown that the solvability is a direct consequence of the algebraic structure. It is conjectured that the Yang-Baxterization of general multi-colour braid-monoid algebras will lead to the construction of further solvable lattice models.

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