An analogue of the classical Yang-Baxter equation for general algebraic structures

Xiaoping Xu

doi:10.1007/bf01293592

An analogue of the classical Yang-Baxter equation for general algebraic structures

Xiaoping Xu

https://doi.org/10.1007/bf01293592

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Journal: Monatshefte fur Mathematik	Publication Date: Dec 1, 1995
Citations: 3

Affiliation: Hong Kong University of Science and Technology, University of Hong Kong

#Vertex Operator #Classical Equation + Show 8 more

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Abstract

In this paper, we introduce an analogue of the classical Yang-Baxter equation for general algebraic structures (including nonassociative algebras and vertex operator algebras). Moreover, we give several ways to construct solutions of the equation in case the algebraic structure is graded by an abelian group. In particular, we construct some unitary nondegenerate trignometric solutions of the classical Yang-Baxter equation for affine Lie algebras by means of our equation.

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