On symmetry properties of Frobenius manifolds and related Lie-algebraic structures
Authors:
- Anatolij K. Prykarpatski,
- Alexander A. Balinsky
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.
- Record ID
- CUTdf0a907ca4a548a6a198e7e7d098eb77
- Publication categories
- ;
- Author
- Journal series
- Symmetry, ISSN , e-ISSN 2073-8994, Monthly
- Issue year
- 2021
- Vol
- 13
- No
- 6
- Pages
- [1-9]
- Article number
- 979
- Other elements of collation
- Bibliografia (na s.) - 8-9; Bibliografia (liczba pozycji) - 41; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 13, Iss. 6, Spec. Iss.
- Substantive notes
- Special Issue: Symmetry of Hamiltonian Systems: Classical and Quantum Aspects
- Keywords in English
- Witten–Dijkgraaf–Verlinde-Verlinde associativity equations, oriented associativity equations, loop lie algebras, Frobenius manifold potential function, Adler–Kostant–Symes scheme, Lie-algeberaic analysis, compatible Hamiltonian flows, reciprocal transformation
- DOI
- DOI:10.3390/sym13060979 Opening in a new tab
- URL
- https://www.mdpi.com/2073-8994/13/6/979/htm Opening in a new tab
- Related project
- Teoria równań i nierówności różniczkowych, układy dynamiczne na rozmaitościach, wybrane działy: analizy matematycznej topologii algebry i geometrii oraz probabilistyki teorii grafów i liczb. . Project leader at PK: , ,
Działalność statutowa - Language
- eng (en) English
- License
- Score (nominal)
- 70
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUTdf0a907ca4a548a6a198e7e7d098eb77/
- URN
urn:pkr-prod:CUTdf0a907ca4a548a6a198e7e7d098eb77
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.