A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation. (English) Zbl 0587.17004

Jimbo, Michio

Lett. Math. Phys. 10, 63-69 (1985).

The author introduces a q-difference analogue of the universal enveloping algebra of a simple Lie algebra. Its representations are studied for the case of sl(2,\({\mathbb{C}})\) and then the theory is applied to determine the trigonometric solutions of the Yang-Baxter equation related to sl(2,\({\mathbb{C}})\) in an arbitrary finite-dimensional irreducible representation.

Reviewer: T.Ratiu

MSC:

17B10	Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B35	Universal enveloping (super)algebras
37J35	Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10	Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35Q99	Partial differential equations of mathematical physics and other areas of application

Keywords:

q-difference analogue; universal enveloping algebra; simple Lie algebra; representations; trigonometric solutions; Yang-Baxter equation

References:

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