2019/10/15 by Fang Li, Siyang Liu, Li, Fang +1 · 1 citation
Mathematics · Physics and Astronomy · #13F60 #16W70 #18E10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.CT #math.RA #math.RT #msc:13F60 #msc:16W70 #msc:18E10
paper · pdf · doi:10.48550/arxiv.1910.06510
18 pages
openalex publication_date 2019/10/15 · arxiv created 2020/04/10 · arxiv updated 2020/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we study the relationship among maximal green sequences, complete forward hom-orthogonal sequences and stability functions in abelian length categories. Mainly, we firstly give a one-to-one correspondence between maximal green sequences and complete forward hom-orthogonal sequences via mutual constructions, and then prove that a maximal green sequence can be induced by a central charge if and only if it satisfies crossing inequalities. As applications, we show that crossing inequalities can be computed by c-vectors for finite dimensional algebras; finally, we give the Rotation Lemma for finite dimensional Jacobian algebras.