The Frobenius-Virasoro algebra and Euler equations

Abstract

We introduce an $\mathfrak{F}$-valued generalization of the Virasoro algebra, called the Frobenius-Virasoro algebra $\mathfrak{vi}{\mathfrak{r}}_{\mathfrak{F}}$, where $\mathfrak{F}$ is a Frobenius algebra over $\mathbb{R}$. We also study Euler equations on the regular dual of $\mathfrak{vi}{\mathfrak{r}}_{\mathfrak{F}}$, including the $\mathfrak{F}$-$\mathrm{KdV}$ equation and the $\mathfrak{F}$-$\mathrm{CH}$ equation and the $\mathfrak{F}$-$\mathrm{HS}$ equation, and discuss their Hamiltonian properties.

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• Bi-Hamiltonian systems on the dual of the Lie algebra of vector fields of the circle and periodic shallow water equations
• Geodesic Flow and Two (Super) Component Analog of the Camassa-Holm Equation
• Novikov algebras and a classification of multicomponent Camassa-Holm equations
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Cited by in corpus (2)

• Integrability of the Frobenius algebra-valued KP hierarchy
• Frobenius manifolds and Frobenius algebra-valued integrable systems