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SUMMARY:Alexander Mikhailov (University of Leeds)
DTSTART:20201209T162000Z
DTEND:20201209T180000Z
DTSTAMP:20260423T023019Z
UID:GDEq/22
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GDEq/22/">Qu
 antisation ideals of nonabelian integrable systems</a>\nby Alexander Mikha
 ilov (University of Leeds) as part of Geometry of differential equations s
 eminar\n\n\nAbstract\nIn my talk I'll discuss a new approach to the proble
 m of quantisation of dynamical systems\, introduce the concept of quantisa
 tion ideals and show meaningful examples. Traditional quantisation theorie
 s start with classical Hamiltonian systems with dynamical variables taking
  values in commutative algebras and then study their non-commutative defor
 mations\, such that the commutators of observables tend to the correspondi
 ng Poisson brackets as the (Planck) constant of deformation goes to zero. 
 I am proposing to depart from systems defined on a free associative algebr
 a. In this approach the quantisation problem is reduced to a description o
 f two-sided ideals which define the commutation relations (the quantisatio
 n ideals) in the quotient algebras and which are invariant with respect to
  the dynamics of the system. Surprisingly this idea works rather efficient
 ly and in a number of cases I have been able to quantise the system\, i.e.
  to find consistent commutation relations for the system.  To illustrate t
 his approach I'll consider the quantisation problem for the non-abelian Bo
 goyavlensky N-chains and other examples\, including quantisation of nonabe
 lian integrable ODEs on free associative algebras.\n\nThe talk is based on
 : AVM\, Quantisation ideals of nonabelian integrable systems\, arXiv prepr
 int <a href="https://arxiv.org/abs/2009.01838">arXiv:2009.01838</a>\, 2020
  (Published in Russ. Math. Surv.  v.75:5\, pp 199-200\, 2020).\n
LOCATION:https://researchseminars.org/talk/GDEq/22/
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