Multi-Colour Braid-Monoid Algebras

Abstract

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.

32 pages

References in corpus (2)

• Solvable lattice models labelled by Dynkin diagrams
• On the construction of integrable dilute ADE models

Cited by in corpus (24)

• Associative-algebraic approach to logarithmic conformal field theories
• New R-matrices from Representations of Braid-Monoid Algebras based on Superalgebras
• Solvable RSOS models based on the dilute BWM algebra
• Fusion of Dilute $A_L$ Lattice Models
• Dilute Birman--Wenzl--Murakami Algebra and $D_{n+1}^{(2)}$ models
• Trigonometric R Matrices related to `Dilute' Birman--Wenzl--Murakami Algebra
• Solutions of the boundary Yang-Baxter equation for ADE models
• A note on graded Yang-Baxter solutions as braid-monoid invariants
• The principal indecomposable modules of the dilute Temperley-Lieb algebra
• The Bubble Algebra: Structure of a Two-Colour Temperley-Lieb Algebra
• Dilute oriented loop models
• $U_q({\mathfrak{sl}}_n)$ web models and ${\mathbb{Z}}_n$ spin interfaces
• Exactly soluble isotropic spin-1/2 ladder models
• Fusion rules for the Temperley-Lieb algebra and its dilute generalisation
• Yang-Baxter algebras based on the two-colour BWM algebra
• Entanglement dynamics in monitored Kitaev circuits: loop models, symmetry classification, and quantum Lifshitz scaling
• Power-law entanglement and Hilbert space fragmentation in non-reciprocal quantum circuits
• A coupled Temperley-Lieb algebra for the superintegrable chiral Potts chain
• Reflection matrices with $U_q[os{p}^{(2)}(2|2m)]$ symmetry
• Critical site percolation on the triangular lattice: From integrability to conformal partition functions
• Fusion hierarchies, $T$-systems and $Y$-systems for the dilute $A_2^{(2)}$ loop models on a strip
• Representations of Two-Colour BWM Algebras and Solvable Lattice Models
• Representation theory for dilute lattice models
• The planar parafermion algebra: The ${\mathbb{Z}}_N$ clock model and the coupled Temperley-Lieb algebra