2015/05/10 by Aslak Bakke Buan, Buan, Aslak Bakke, Yann Palu +3
Mathematics · #16E35 #16G20 #16G70 #18E30 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1505.02357
openalex publication_date 2015/05/10 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We give a complete classification of all algebras appearing as endomorphism algebras of maximal rigid objects in standard 2-Calabi-Yau categories of finite type. Such categories are equivalent to certain orbit categories of derived categories of Dynkin algebras. It turns out that with one exception, all the algebras that occur are 2-Calabi-Yau-tilted, and therefore appear in an earlier classification by Bertani-Økland and Oppermann. We explain this phenomenon by investigating the subcategories generated by rigid objects in standard 2-Calabi-Yau categories of finite type.