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Keywords = Frobenius manifold potential function

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9 pages, 281 KB  
Article
On Symmetry Properties of Frobenius Manifolds and Related Lie-Algebraic Structures
by Anatolij K. Prykarpatski and Alexander A. Balinsky
Symmetry 2021, 13(6), 979; https://doi.org/10.3390/sym13060979 - 31 May 2021
Cited by 2 | Viewed by 2677
Abstract
The aim of this paper is to develop an algebraically feasible approach to solutions of the oriented associativity equations. Our approach was based on a modification of the Adler–Kostant–Symes integrability scheme and applied to the co-adjoint orbits of the diffeomorphism loop group of [...] Read more.
The aim of this paper is to develop an algebraically feasible approach to solutions of the oriented associativity equations. Our approach was based on a modification of the Adler–Kostant–Symes integrability scheme and applied to the co-adjoint orbits of the diffeomorphism loop group of the circle. A new two-parametric hierarchy of commuting to each other Monge type Hamiltonian vector fields is constructed. This hierarchy, jointly with a specially constructed reciprocal transformation, produces a Frobenius manifold potential function in terms of solutions of these Monge type Hamiltonian systems. Full article
(This article belongs to the Special Issue Symmetry of Hamiltonian Systems: Classical and Quantum Aspects)
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