The No Gap Conjecture for tame hereditary algebras |
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Authors: | Stephen Hermes Kiyoshi Igusa |
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Institution: | 1. Department of Mathematics, Wellesley College, Wellesley, MA 02481, United States of America;2. Department of Mathematics, Brandeis University, Waltham, MA 02454, United States of America |
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Abstract: | The “No Gap Conjecture” of Brüstle–Dupont–Pérotin states that the set of lengths of maximal green sequences for hereditary algebras over an algebraically closed field has no gaps. This follows from a stronger conjecture that any two maximal green sequences can be “polygonally deformed” into each other. We prove this stronger conjecture for all tame hereditary algebras over any field, equivalently, for any acyclic tame skew-symmetrizable exchange matrix. |
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Keywords: | 16G20 20F55 |
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