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.

arXiv comment2 pages, accepted for publication by Russian Mathematical Surveys

References in corpus (2)

• Nonabelian Integrable Systems, Quasideterminants, and Marchenko Lemma
• Integrable ODEs on Associative Algebras

Cited by in corpus (6)

• On non-abelian quadrirational Yang-Baxter maps
• Non-Abelian evolution systems with conservation laws
• On matrix Painlevé-4 equations. Part 2: Isomonodromic Lax pairs
• On matrix Painlevé-4 equations. Part 1: Painlevé--Kovalevskaya test
• Quantisations of the Volterra hierarchy
• KdV hierarchies and quantum Novikov's equations