On symmetry properties of frobenius manifolds and related lie-algebraic structures

Prykarpatski, Anatolij K. and Balinsky, Alexander A. ORCID: https://orcid.org/0000-0002-8151-4462 2021. On symmetry properties of frobenius manifolds and related lie-algebraic structures. Symmetry 13 (6) , 979. 10.3390/sym13060979

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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 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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	MDPI
ISSN:	2073-8994
Date of First Compliant Deposit:	2 June 2021
Date of Acceptance:	21 May 2021
Last Modified:	06 May 2023 07:57
URI:	https://orca.cardiff.ac.uk/id/eprint/141709

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