Ladders and simplicity of derived module categories
Ladders and simplicity of derived module categories
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DOI：
10.1016/j.jalgebra.2016.10.023
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发表时间：
2013-10
期刊：
影响因子：
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通讯作者：
Lidia Angeleri Hugel;S. Koenig;Qunhua Liu;D. Yang
中科院分区：
文献类型：
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作者：
Lidia Angeleri Hugel;S. Koenig;Qunhua Liu;D. Yang
利用一种新的技术，即最大突变序列的重排序，研究了导出模范畴的重排序。显示阶梯中的位置是为了控制一个子元素是否限制从无界到另一个级别的派生类别。梯子也在各个层面上控制着衍生的简单性。一个代数是导出单的，如果它的导出范畴不能被解构，也就是说，如果它不是一个非平凡元的中间项，而这个非平凡元的外部项又是代数的导出范畴。导出的简单性在每一个层次上的特点是在高度的ladder.These结果的补充，提供新的类的例子导出简单的环，特别是不可分解的交换环，以及有限维反例的约旦-Hölder问题的导出模范畴。此外，矩阵元用于计算同调和K-理论不变量。
Recollements of derived module categories are investigated, using a new technique, ladders of recollements, which are maximal mutation sequences. The position in the ladder is shown to control whether a recollement restricts from unbounded to another level of derived category. Ladders also turn out to control derived simplicity on all levels. An algebra is derived simple if its derived category cannot be deconstructed, that is, if it is not the middle term of a non-trivial recollement whose outer terms are again derived categories of algebras. Derived simplicity on each level is characterised in terms of heights of ladders.These results are complemented by providing new classes of examples of derived simple rings, in particular indecomposable commutative rings, as well as by a finite dimensional counterexample to the Jordan–Hölder problem for derived module categories. Moreover, recollements are used to compute homological and K-theoretic invariants.