2018/03/08 by Hideto Asashiba, Asashiba, H., Mayumi Kimura +5
Mathematics · Physics and Astronomy · #16W20 #16W22 #16W50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1803.02969
openalex publication_date 2018/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Assume that a basic algebra A over an algebraically closed field \Bbbk with a basic set A0 of primitive idempotents has the property that eAe=\Bbbk for all e ∈ A0. Let n be a nonzero integer, and ϕ and ψ two automorphisms of the repetitive category A of A with jump n (namely, they send A[0] to A[n], where A[i] is the i-th copy of A in A for all i ∈ ℤ). If ϕ and ψ coincide on the objects and if there exists a map ρ\colon A0 → \Bbbk such that ρ0(y)ϕ0(a)=ψ0(a)ρ0(x) for all morphisms a∈ A(x,y), then the orbit categories A/⟨ ϕ⟩ and A/⟨ ψ⟩ are isomorphic as ℤ-graded categories.