1993/03/30 by Uwe Grimm, Paul A. Pearce · 1 citation
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic number #Algebraic structure #Algebraic structures and combinatorial models #Braid #Braid group #Braid theory #Free monoid #Lattice (music) #Mathematics #Monoid #Nonlinear Waves and Solitons #Physics #Pure mathematics #hep-th #math.QA
paper · pdf · doi:10.1088/0305-4470/26/24/018
published as J.Phys. A26 (1993) 7435-7460 · 32 pages
arxiv created 1993/03/30 · openalex publication_date 1993/12/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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(1992) as well as by Roche(1992). 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 Baxterization of general multi-colour braid-monoid algebras will lead to the construction of further solvable lattice models.