spherical objects of the multiplicity free brauer tree algebra with two edges
首发时间:2018-07-09
abstract:spherical objects and tilting objects are important concepts in derived categories. they induce derived equivalences by taking derived tensor and mapping cone respectively. in this paper we explicitly describe, using the socalled n-complex, all spherical objects and tilting objects of the multiplicity free brauer tree algebra with two edges. this algebra is morita equivalent to the path algebra of a 2-cycle modulo the admissible ideal generated by the paths of length 3. we find the spherical objects are precisely the indecomposable direct summands of the tilting objects.
keywords: brauer tree algebra; spherical object;tilting object;derived picard group;n-complex
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带两条边且无重数的brauer树代数上的球面对象
摘要:球面对象和倾斜对象是导出范畴中重要的概念,它们可以分别通过取导出张量函子和映射锥得到导出等价。本文中我们将借助于n- 复形详细描述一个brauer树代数上所有的球面对象和倾斜对象,即对应于带两条边且无重数的树的brauer代数,它morita等价于长为2的定向圈的路代数模去由长为3 的道路生成的容许理想。我们发现它的球面对象恰为倾斜对象的不可分解直和项。
关键词: brauer树代数 球面对象 倾斜对象 导出picard 群 n-复形
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