2010/02/25 by Michael Barot, Barot, Michael, Sonia Trepode +1 · 1 citation
Mathematics · Physics and Astronomy · #16G20 #18E30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #math.RT #msc:16G20 #msc:18E30
paper · pdf · doi:10.48550/arxiv.1002.4842
14 pages, 8 figures
openalex publication_date 2010/02/25 · arxiv created 2011/10/22 · arxiv updated 2011/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In association with a finite dimensional algebra A of global dimension two, we consider the endomorphism algebra of A, viewed as an object in the triangulated hull of the orbit category of the bounded derived category, in the sense of Amiot. We characterize the algebras A of global dimension two such that its endomorphism algebra is isomorphic to a cluster-tilted algebra with a cyclically oriented quiver.Furthermore, in the case that the cluster tilted algebra with a cyclically oriented quiver is of Dynkin or extended Dynkin type then A is derived equivalent to a hereditary algebra of the same type.