Duality on operator Frobenius algebras solves the Eisenhart-Stäckel problem by classifying all nondegenerate finite-dimensional integrable systems with quadratic integrals where the associated (1,1)-tensors commute.
The geometry of Hamiltonian systems of hydrodynamic type. The generalized hodograph method
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Duality of operator Frobenius algebras and solution of Eisenhart-St\"ackel problem in the non-diagonal case
Duality on operator Frobenius algebras solves the Eisenhart-Stäckel problem by classifying all nondegenerate finite-dimensional integrable systems with quadratic integrals where the associated (1,1)-tensors commute.