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Pick a curve (from the list, or type its Gauss word), then a grading, then which regions to fill. Everything computed for that configuration appears together: the region table, the polygon list, the complete A∞ operation table, and, for the worked examples, the deformed family.
Type any signed Gauss word with at most four double points, in any labelling: it is matched to the stored curve up to relabelling, sign flip, rotation and reversal.
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Alg₂ … Alg₅
An arrow A → B means that B lies in the closure of the orbit of A. On the right, Aut is the dimension of the automorphism group of the algebras in that row and orbit the dimension of their orbit in the variety of unital algebra structures on kn (unit fixed; Aut + orbit = n² − n). A dot is a factor k; framed nodes are the generic algebras of the irreducible components; ×N counts the entries of this database with that degree-zero algebra. Click a node to browse them.
Alg₂
Alg₃
Alg₄
Alg₅
occurs in this database no entry in this database×N = witness entries in this database