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arXiv · 1504.01284

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

Mahouton Norbert Hounkonnou·Partha Guha·Tudor Ratiu
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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 $\rho-$compatibility equation and perform a phase-space extension. Finally, concrete relevant particular cases are investigated.

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Mahouton Norbert Hounkonnou, Partha Guha, Tudor Ratiu. 2015-04-06. Generalized Virasoro algebra: left-symmetry and related algebraic and hydrodynamic properties. https://arxiv.org/abs/1504.01284

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