Derived-tame algebras and non-commutative nodal projective curves

导出驯服代数和非交换节点射影曲线

• 批准号: 283334198
• 负责人: Professor Dr. Igor Burban
• 金额: --
• 依托单位: Fachgebiet Computeralgebra und Zahlentheorie
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2015
• 资助国家: 德国
• 起止时间: 2014-12-31 至 2018-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/283334198?language=en
• 关键词: Derived; tame; algebras; non; commutative

The goal of this project is to develop a systematic theory of non-commutative nodal projective curves, similar to the theory of weighted projective lines of Geigle and Lenzing. In particular, we want to clarify when the derived category of coherent sheaves on such a curve admits a tilting object, and describe the classes of tilted algebras arising in this way. We are especially interested in the case when the non-commutative nodal curve we start with (and as a result, the corresponding tilted algebra) has tame derived representation type.Using this approach, we anticipate to treat with new methods old problems about spherical objects and auto-equivalences of the derived category of coherent sheaves on a cycle of projective lines.

该项目的目的是开发一种非交互性淋巴结射击曲线的系统理论，类似于吉格尔和Lenzing的加权投影线理论。特别是，我们要澄清何时在这样的曲线上衍生的连贯滑轮类别允许倾斜对象，并描述以这种方式产生的倾斜代数的类别。当我们从我们开始（结果，相应的倾斜代数）具有驯服的表示类型（因此，我们希望使用这种方法来治疗有关球形对象的新方法和关于相干性类别的较新方法，我们预计在投影线周期的衍生类别。