Next Article in Journal / Special Issue
Bundles over Quantum RealWeighted Projective Spaces
Previous Article in Journal / Special Issue
The Duality between Corings and Ring Extensions
Article Menu

Export Article

Open AccessArticle
Axioms 2012, 1(2), 186-200; doi:10.3390/axioms1020186

From Coalgebra to Bialgebra for the Six-Vertex Model: The Star-Triangle Relation as a Necessary Condition for Commuting Transfer Matrices

Departments of Physics and Mathematics, University of Wisconsin-Parkside 900 Wood Road, Kenosha, WI 53141, USA
Received: 2 July 2012 / Revised: 7 August 2012 / Accepted: 16 August 2012 / Published: 27 August 2012
(This article belongs to the Special Issue Hopf Algebras, Quantum Groups and Yang-Baxter Equations)
View Full-Text   |   Download PDF [200 KB, uploaded 27 August 2012]

Abstract

Using the most elementary methods and considerations, the solution of the star-triangle condition (a2+b2-c2)/2ab = ((a’)^2+(b’)^2-(c’))^2/2a’b’ is shown to be a necessary condition for the extension of the operator coalgebra of the six-vertex model to a bialgebra. A portion of the bialgebra acts as a spectrum-generating algebra for the algebraic Bethe ansatz, with which higher-dimensional representations of the bialgebra can be constructed. The star-triangle relation is proved to be necessary for the commutativity of the transfer matrices T(a, b, c) and T(a’, b’, c’).
Keywords: vertex model; bialgebra; coalgebra; Bethe ansatz vertex model; bialgebra; coalgebra; Bethe ansatz
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Schmidt, J.R. From Coalgebra to Bialgebra for the Six-Vertex Model: The Star-Triangle Relation as a Necessary Condition for Commuting Transfer Matrices. Axioms 2012, 1, 186-200.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Axioms EISSN 2075-1680 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top