题目： Recollements and idempotent ideals
报告人： Prof. Dr. Steffen Koenig (University of Stuttgart, Germany)
When studying module categories of algebras, two kinds of recollements are used; recollements of abelian categories, where all three terms are module categories, and recollements of triangulated categories, where all three terms are derived module categories. Psaroudakis and Vitória have shown that there is a normal form for these abelian recollements: they are equivalent to recollements induced by idempotent ideals. An analogue for the recollements of derived module categories is, however, not true.
In joint work with L.Angeleri, Q.Liu and D.Yang, a characterisation has been given of recollements of derived module categories that are equivalent to recollements induced by (stratifying) idempotent ideals. This complements results by Psaroudakis and Vitória who have established such normal forms for particular classes of algebras. After explaining this characterisation, some methods will be explained to change a recollement into an equivalent one.