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Title: Purely non-local Hamiltonian formalism, Kohno connections and ∨-systems

In this paper, we extend purely non-local Hamiltonian formalism to a class of Riemannian F-manifolds, without assumptions on the semisimplicity of the product ○ or on the flatness of the connection ∇. In the flat case, we show that the recurrence relations for the principal hierarchy can be re-interpreted using a local and purely non-local Hamiltonian operators and in this case they split into two Lenard-Magri chains, one involving the even terms, the other involving the odd terms. Furthermore, we give an elementary proof that the Kohno property and the ∨-system condition are equivalent under suitable assumptions and we show how to associate a purely non-local Hamiltonian structure to any ∨-system, including degenerate ones.
Authors:
 [1] ;  [2]
  1. Department of Mathematics and Statistics, University of Toledo, 2801 W. Bancroft St., 43606 Toledo, Ohio (United States)
  2. Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Via Roberto Cozzi 53, I-20125 Milano (Italy)
Publication Date:
OSTI Identifier:
22405047
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 11; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHAINS; HAMILTONIAN FUNCTION; HAMILTONIANS; MATHEMATICAL MANIFOLDS; RECURSION RELATIONS