Quantisation ideals of nonabelian integrable systems

Abstract

We consider dynamical systems on the space of functions taking values in a free associative algebra. The system is said to be integrable if it possesses an infinite dimensional Lie algebra of commuting symmetries. In this paper we propose a new approach to the problem of quantisation of dynamical systems, introduce the concept of quantisation ideals and provide meaningful examples.

2 pages, accepted for publication by Russian Mathematical Surveys

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• Quantisations of the Volterra hierarchy
• KdV hierarchies and quantum Novikov's equations