A straightforward construction of Z-graded Lie algebras of full-fledged nonlocal symmetries via recursion operators

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F25%3AA0000184" target="_blank" >RIV/47813059:19610/25:A0000184 - isvavai.cz</a>

Result on the web

<a href="https://www.sciencedirect.com/science/article/pii/S016727892500137X" target="_blank" >https://www.sciencedirect.com/science/article/pii/S016727892500137X</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.physd.2025.134658" target="_blank" >10.1016/j.physd.2025.134658</a>

Result language

angličtina

Original language name

A straightforward construction of Z-graded Lie algebras of full-fledged nonlocal symmetries via recursion operators

Original language description

We consider the reduced quasi-classical self-dual Yang–Mills equation (rYME) and two recently found (Jahnová and Vojčák, 2024) invertible recursion operators Rq and Rm for its full-fledged (in a given differential covering) nonlocal symmetries. We introduce a Z-grading on the Lie algebra symLτ(E) of all nonlocal Laurent polynomial symmetries of the rYME and prove that both the operators Rq and Rm are Z-graded automorphisms of the underlying vector space on the set symLτ(E). This inter alia implies that all its vector subspaces formed by all homogeneous elements of a given fixed degree (i.e. a weight in the context below) are mutually isomorphic, and thus each of them can be uniquely reconstructed from the vector space of all homogeneous symmetries of the zero degree. To the best of our knowledge, such a result is unparalleled in the current body of literature. The obtained results are used for the construction of a Lie subalgebra V of symLτ(E) which contains all known to us nonlocal Laurent polynomial symmetries of the rYME. The Lie algebra V is subsequently described as the linear span of the orbits of a set of selected zero-weight symmetries — we refer to them as to the seed generators of V. Further, we study the hierarchies of symmetries related to the seed generators under the action of the group of recursion operators generated by Rq and Rm. Finally, the linear dependence/independence of the (sub)set of generators of V is discussed.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2025

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Physica D: Nonlinear Phenomena

ISSN

0167-2789

e-ISSN

1872-8022

Volume of the periodical

476

Issue of the periodical within the volume

June

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

14

Pages from-to

„134658-14“-„134658-14“

UT code for WoS article

001475789500001

EID of the result in the Scopus database

2-s2.0-105002816631