AI 中文总结
研究温和代数上倾斜模及其自同态代数，利用标记曲面与平铺框架，证明平铺忠实剖分对应倾斜模，定义辅助代数并证其与自同态代数同构，构造新平铺，引入保持翻转的倾斜模。
AI 中文摘要
本文在Baur和Simões引入的标记曲面与平铺框架下研究温和代数上的倾斜模及其自同态代数。证明了平铺的忠实剖分对应于倾斜模。对于一个忠实剖分，定义了一个辅助代数并证明其与相应倾斜模的自同态代数同构。还构造了一个实现此自同态代数的新平铺，并引入了保持翻转的倾斜模。
英文摘要
This paper investigates tilting modules over gentle algebras and their endomorphism algebras within the framework of marked surfaces and tilings introduced by Baur and Simões. Faithful dissections of a tiling are shown to correspond to tilting modules. For a faithful dissection, we define an auxiliary algebra and prove that it is isomorphic to the endomorphism algebra of the corresponding tilting module. We also construct a new tiling realizing this endomorphism algebra and introduce a flip preserving tilting modules.
Comments25 pages, comments welcome
