Algebraic Structure of Integrable Systems in Multidimensions

摘要

The d-simplex equations are multidimensional generalizations of the Yang-Baxter (triangle) equations. We discuss the algebraic structure of the hierarchy of the d-simplex equations and their relevance to the notion of quantum and classical integrability. A multidimensional generalization of the notion of lax pair is given. 7 refs. (ERA citation 14:023523)