On compact exceptional objects in derived module categories

Abstract

Let $A$ be a finite dimensional algebra and $D^b(A)$ be the bounded derived category of finitely generated left $A$-modules. In this paper we consider lengths of compact exceptional objects in $D^b(A)$, proving a sufficient condition such that these lengths are bounded by the number of isomorphism classes of simple $A$-modules. Moreover, we show that algebras satisfying this condition is bounded derived simple.

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References in corpus (4)

• Rigidity of tilting complexes and derived equivalence for self-injective algebras
• Ladders and simplicity of derived module categories
• Infinitely many algebras derived equivalent to a block
• Stratifications of algebras with two simple modules