On symmetry properties of Frobenius manifolds and related Lie-algebraic structures / Anatolij K. Prykarpatski, Alexander A. Balinsky // Symmetry [Dokument elektroniczny]. – 2021, Vol. 13, Iss. 6, Spec. ... więcej

On symmetry properties of Frobenius manifolds and related Lie-algebraic structures / Anatolij K. Prykarpatski, Alexander A. Balinsky // Symmetry [Dokument elektroniczny]. – 2021, Vol. 13, Iss. 6, Spec. Iss., 9 s. – Tryb dostępu: https://www.mdpi.com/2073-8994/13/6/979/htm. – Oznaczenie ref./art.: 979. – Bibliogr. 41 poz., Abstr. – Special Issue: Symmetry of Hamiltonian Systems: Classical and Quantum Aspects. – doi: 10.3390/sym13060979. – ISSN 2073-8994

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 ... więcej

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.