Generalized Virasoro algebra: left-symmetry and related algebraic and hydrodynamic properties

DOI

10.1080/14029251.2016.1135642How to use a DOI?

Keywords

Virasoro algebra; Left-symmetric algebras; Quasi-associativity; Coboundary operators; Nonlinear systems of hydrodynamic type

Abstract

Motivated by the work of Kupershmidt (J. Nonlin. Math. Phys. 6 (1998), 222 –245) we discuss the occurrence of left symmetry in a generalized Virasoro algebra. The multiplication rule is defined, which is necessary and sufficient for this algebra to be quasi-associative. Its link to geometry and nonlinear systems of hydrodynamic type is also recalled. Further, the criteria of skew-symmetry, derivation and Jacobi identity making this algebra into a Lie algebra are derived. The coboundary operators are defined and discussed. We deduce the hereditary operator and its generalization to the corresponding 3–ary bracket. Further, we derive the so-called ρ–compatibility equation and perform a phase-space extension. Finally, concrete relevant particular cases are investigated.

Copyright

© 2016 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Mahouton Norbert Hounkonnou
AU  - Partha Guha
AU  - Tudor Ratiu
PY  - 2021
DA  - 2021/01/06
TI  - Generalized Virasoro algebra: left-symmetry and related algebraic and hydrodynamic properties
JO  - Journal of Nonlinear Mathematical Physics
SP  - 47
EP  - 73
VL  - 23
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2016.1135642
DO  - 10.1080/14029251.2016.1135642
ID  - Hounkonnou2021
ER  -