Generalized Virasoro algebra: left-symmetry and related algebraic and hydrodynamic properties
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 ary bracket. Further, we derive the so-called compatibility equation and perform a phase-space extension. Finally, concrete relevant particular cases are investigated.
Keywords
Cite
@article{arxiv.1504.01284,
title = {Generalized Virasoro algebra: left-symmetry and related algebraic and hydrodynamic properties},
author = {Mahouton Norbert Hounkonnou and Partha Guha and Tudor Ratiu},
journal= {arXiv preprint arXiv:1504.01284},
year = {2015}
}