In this paper we determine extensions of higher degree between indecomposable modules over gentle algebras. In particular, our results show how such extensions either eventually vanish or become periodic. We give a geometric interpretation of vanishing and periodicity of higher extensions in terms of the surface underlying the gentle algebra. For gentle algebras arising from triangulations of surfaces, we give an explicit basis of higher extension spaces between indecomposable modules showing that in this case there is a symmetry of the higher extension spaces.

中文翻译：

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温和代数的更高扩展

在本文中，我们确定了不可分解模块之间在温和代数上的更高程度的扩展。特别是，我们的结果显示了这种扩展如何最终消失或变得周期性。我们根据温和代数下的表面给出了更高扩展的消失和周期性的几何解释。对于由曲面三角剖分产生的温和代数，我们给出了不可分解模块之间的更高扩展空间的明确基础，表明在这种情况下存在更高扩展空间的对称性。