Derived categories of quasi-hereditary algebras and their derived composition series
Derived categories of quasi-hereditary algebras and their derived composition series
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DOI：
10.4171/171-1/11
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发表时间：
2016-03
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通讯作者：
Martin Kalck
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文献类型：
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作者：
Martin Kalck
本文研究了拟遗传代数在Angeleri H ugel，K onig&Liu意义下的导模范畴的合成列.更确切地说，我们证明了，有一个合成系列的所有因素是派生范畴的向量空间不派生范畴的拟遗传代数。这对Liu&Yang的一个问题给出了否定的回答，证明也证实了Bobi\'nski &Malicki的一个猜想的一部分。在另一个方向上，我们证明了拟遗传代数的导出范畴可以有许多不同长度和合成因子的合成序列。也就是说，拟遗传代数的导范畴的合成列不存在Jordan-H“older性质.
We study composition series of derived module categories in the sense of Angeleri H\"ugel, K\"onig&Liu for quasi-hereditary algebras. More precisely, we show that having a composition series with all factors being derived categories of vector spaces does not characterise derived categories of quasi-hereditay algebras. This gives a negative answer to a question of Liu&Yang and the proof also confirms part of a conjecture of Bobi\'nski&Malicki. In another direction, we show that derived categories of quasi-hereditary algebras can have composition series with lots of different lengths and composition factors. In other words, there is no Jordan-H\"older property for composition series of derived categories of quasi-hereditary algebras.