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.
St¨ ackel problem for non-diagonal Killing tensors: Yano-Patterson lifts, algebra of strong symmetries and quadratic in momenta integrals
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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.