The naive approach for constructing the derived category of a d-abelian category fails

2016/04/12 by Jasso, Gustavo, Külshammer, Julian · 1 citation
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1604.03473

Abstract

Let k be a field. In this short note we give an example of a 2-abelian k-category, realized as a 2-cluster-tilting subcategory of the category mod A of finite dimensional (right) A-modules over a finite dimensional k-algebra A, for which the naive idea for constructing its "bounded derived category" as 2-cluster-tilting subcategory of the bounded derived category of mod A cannot work.

Cited by

• Replicated algebras derived equivalent to higher Auslander algebras of type A

Related

• The completion of d-abelian categories
• Construction of d-abelian categories via derived categories
• Projectively generated d-abelian categories are d-cluster tilting
• Abelian subcategories of triangulated categories induced by simple minded systems
• Wide subcategories of d-cluster tilting subcategories