All non-degenerate second-order maximally superintegrable systems in three dimensions arise from semi-simple and nilpotent Frobenius structures via conification and direct-product constructions.
An algebraic geometric classification of superin- tegrable systems in the Euclidean plane
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Second-order superintegrable systems from semi-simple and nilpotent Frobenius structures
All non-degenerate second-order maximally superintegrable systems in three dimensions arise from semi-simple and nilpotent Frobenius structures via conification and direct-product constructions.