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1990•International Journal of Modern Physics ARequires access

QUASITRIANGULAR HOPF ALGEBRAS AND YANG-BAXTER EQUATIONS

Shahn Majid

Open publisher page 416 citations

Abstract

This is an informal introduction to the theory of quasitriangular Hopf algebras and its connections with physics. Basic properties and applications of Hopf algebras and Yang-Baxter equations are reviewed, with the quantum group Uq(sl2) as a frequent example. The development builds up to the representation theory of quasitriangular Hopf algebras. Much of the abstract representation theory is new, including a formula for the rank of a representation.

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What this paper is about

This is an informal introduction to the theory of quasitriangular Hopf algebras and its connections with physics. Basic properties and applications of Hopf algebras and Yang-Baxter equations are reviewed, with the quantum group Uq(sl2) as a frequent example. The development builds up to the representation theory of quasitriangular Hopf algebras. Much of the abstract representation theory is new, including a formula for the rank of a representation.

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OpenAlex reports 416 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This is an informal introduction to the theory of quasitriangular Hopf algebras and its connections with physics. Basic properties and applications of Hopf algebras and Yang-Baxter equations are reviewed, with the quantum group Uq(sl2) as a frequent example. The development builds up to the representation theory of quasitriangular Hopf algebras. Much of the abstract representation theory is new, including a formula for the rank of a representation.

Key concepts: Quasitriangular Hopf algebra, Hopf algebra, Quantum group, Representation theory of Hopf algebras, Representation (politics), Rank (graph theory), Pure mathematics, Representation theory

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