Symmetry and Integrability

A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: closed (30 November 2015) | Viewed by 4210

Special Issue Editor


E-Mail Website
Guest Editor
Department of Mathematics, Kinki University, Kowakae 3-4-1, Higashi-Osaka 577-8502, Japan

Special Issue Information

Dear Colleagues,

Symmetry is one of the most essential ingredients of integrability. By the very definition of integrability, integrable systems have Abelian symmetries as a consequence of the existence of conservation laws. Moreover, since the late 1970s, diverse types of non-Abelian symmetries have been discovered. Those non-Abelian symmetries are accompanied by particular algebraic structures. For instance, integrable many-body problems of the Calogero and Toda type are characterized by simple Lie algebras and associated Weyl groups. This is also the case for the 1+1 dimensional Drinfeld-Sokolov hierarchies. The 1+2 dimensional KP and Toda hierarchies and 1+1 dimensional reductions thereof are governed by infinite dimensional general linear, orthogonal and affine algebras. In quantum integrable systems, these Lie algebraic structures are deformed to “quantum algebras”, i.e., Yangians, quantum affine algebras, and their elliptic analogs. In a different context, quantization of the Drinfeld-Sokolov hierarchies is linked with symmetry algebras of conformal field theories. This Special Issue is devoted to more recent progress of these subjects and related issues.

Prof. Dr. Kanehisa Takasaki
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • classical and quantum integrable systems
  • solvable statistical models
  • conformal field theories
  • non-Abelian symmetries
  • discrete symmetries
  • simple and affine Lie algebras
  • vertex operators
  • Yangian, quantum affine and elliptic algebras
  • Virasoro and W algebras
  • Weyl groups, Coxeter groups and Hecke algebras

Published Papers (1 paper)

Order results
Result details
Select all
Export citation of selected articles as:

Research

254 KiB  
Article
Low Dimensional Vessiot-Guldberg-Lie Algebras of Second-Order Ordinary Differential Equations
by Rutwig Campoamor-Stursberg
Symmetry 2016, 8(3), 15; https://doi.org/10.3390/sym8030015 - 17 Mar 2016
Cited by 5 | Viewed by 3764
Abstract
A direct approach to non-linear second-order ordinary differential equations admitting a superposition principle is developed by means of Vessiot-Guldberg-Lie algebras of a dimension not exceeding three. This procedure allows us to describe generic types of second-order ordinary differential equations subjected to some constraints [...] Read more.
A direct approach to non-linear second-order ordinary differential equations admitting a superposition principle is developed by means of Vessiot-Guldberg-Lie algebras of a dimension not exceeding three. This procedure allows us to describe generic types of second-order ordinary differential equations subjected to some constraints and admitting a given Lie algebra as Vessiot-Guldberg-Lie algebra. In particular, well-known types, such as the Milne-Pinney or Kummer-Schwarz equations, are recovered as special cases of this classification. The analogous problem for systems of second-order differential equations in the real plane is considered for a special case that enlarges the generalized Ermakov systems. Full article
(This article belongs to the Special Issue Symmetry and Integrability)
Back to TopTop