5 citations · 5 across the 4 of their papers we have counts for
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Discrete differential-geometric Poisson brackets: general theory and explicit constructions
Marta Dell'Atti, Giorgio Gubbiotti, Pierandrea Vergallo
We review the discrete theory of differential-geometric Poisson brackets as introduced by B. A. Dubrovin, and we present a complete proof of their characterisation in the non-degen…
Classification of pairs of second-order Hamiltonian operators and hydrodynamic type systems in six components
Giorgio Gubbiotti, Lambertus Van Geemen, Pierandrea Vergallo
Following a recent characterisation of hydrodynamic systems with second-order Hamiltonian structure in terms of alternating three-forms on the projective space, we present a comple…
A novel chain of Lie algebras and its coalgebra symmetry
Giorgio Gubbiotti, Danilo Latini, Bert van Geemen
We study a novel -dimensional non-semisimple Lie algebra , a generalisation of both and the two-photon Lie algebra $\mathfra…
Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators
Giorgio Gubbiotti, Francesco Oliveri, Emanuele Sgroi +1
We study from an algebraic and geometric viewpoint Hamiltonian operators which are sum of a non-degenerate first-order homogeneous operator and a Poisson tensor. In flat coordinate…
Line geometry of pairs of second-order Hamiltonian operators and quasilinear systems
Giorgio Gubbiotti, Bert van Geemen, Pierandrea Vergallo
We demonstrate that a pair consisting of a second-order homogeneous Hamiltonian structure in components and its associated system of conservation laws is in bijective correspon…