On compact exceptional objects in derived module categories

2013/12/06 by Liping Li, Li, Liping
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Nonlinear Waves and Solitons #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1312.1762

openalex publication_date 2013/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Ladders and simplicity of derived module categories
• Rigidity of tilting complexes and derived equivalence for self-injective algebras
• Stratifications of algebras with two simple modules

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