Affine Quantum Groups

Research output: Contribution to journalArticle

Author(s)

Department/unit(s)

Publication details

JournalEncyclopedia of Mathematical Physics
DateE-pub ahead of print - 18 Jul 2006
DatePublished (current) - 2006
Number of pages8
Pages (from-to)183-190
Early online date18/07/06
Original languageEnglish

Abstract

Affine quantum groups are certain pseudo-quasitriangular Hopf algebras that arise in mathematical physics in the context of integrable quantum field theory, integrable quantum spin chains, and solvable lattice models. They provide the algebraic framework behind the spectral parameter dependent Yang-Baxter equation. One can distinguish three classes of affine quantum groups, each leading to a different dependence of the R-matrices on the spectral parameter: Yangians lead to rational R-matrices, quantum affine algebras lead to trigonometric R-matrices and elliptic quantum groups lead to elliptic R-matrices. We will mostly concentrate on the quantum affine algebras but many results hold similarly for the other classes. After giving mathematical details about quantum affine algebras and Yangians in the first two section, we describe how these algebras arise in different areas of mathematical physics in the three following sections. We end with a description of boundary quantum groups which extend the formalism to the boundary Yang-Baxter (reflection) equation.

    Research areas

  • Mathematical Physics

Discover related content

Find related publications, people, projects, datasets and more using interactive charts.

View graph of relations