Derived categories of quasi-hereditary algebras and their derived composition series [chapter]

Martin Kalck
Representation Theory – Current Trends and Perspectives  
We study composition series of derived module categories in the sense of Angeleri Hügel, König & 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 Bobiński & Malicki. In another direction, we show that derived
more » ... t 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-Hölder property for composition series of derived categories of quasi-hereditary algebras.
doi:10.4171/171-1/11 fatcat:hspqek6qovclzjfvijeahw6wpm