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.
Varieties of sums of powers
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Generalizes Iarrobino's symmetric decomposition to self-dual modules over local algebras, classifies local Hilbert functions for small degrees, and extends Kunte's self-duality criterion.
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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.
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Iarrobino's symmetric decomposition for self-dual modules
Generalizes Iarrobino's symmetric decomposition to self-dual modules over local algebras, classifies local Hilbert functions for small degrees, and extends Kunte's self-duality criterion.