2018/11/12 by Huanhuan Li, Li, Huanhuan
Mathematics · #16E45 #16G20 #18E30 #18G35 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT #msc:16E45 #msc:16G20 #msc:18E30 #msc:18G35
paper · pdf · doi:10.48550/arxiv.1811.04542
arXiv admin note: text overlap with arXiv:1512.04178, arXiv:1610.00144; text overlap with arXiv:1301.0195 by other authors
arxiv created 2018/11/12 · openalex publication_date 2018/11/12 · arxiv updated 2018/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a certain finite graph E, we consider the corresponding finite dimensional algebra A with radical square zero. An explicit compact generator for the homotopy category of acyclic complexes of injective (resp. projective) modules over A, called the injective (resp. projective) Leavitt complex of E, was constructed in [18] (resp. [19]). We overview the connection between the injective (resp. projective) Leavitt complex and the Leavitt path algebra of E. A differential graded bimodule structure, which is right quasi-balanced, is endowed to the injective (resp. projective) Leavitt complex in [18] (resp. [19]). We prove that the injective (resp. projective) Leavitt complex is not left quasi-balanced.