Gorenstein properties of simple gluing algebras

2017/01/31 by Ming Lu, Lu, Ming · 1 citation
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1701.09074

openalex publication_date 2017/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A=KQ_A/I_A and B=KQ_B/I_B be two finite-dimensional bound quiver algebras, fix two vertices a∈ Q_A and b∈ Q_B. We define an algebra Λ=KQ_Λ/I_Λ, which is called a simple gluing algebra of A and B, where Q_Λ is from Q_A and Q_B by identifying a and b, I_Λ=⟨ I_A,I_B⟩. We prove that Λ is Gorenstein if and only if A and B are Gorenstein, and describe the Gorenstein projective modules, singularity category, Gorenstein defect category and also Cohen-Macaulay Auslander algebra of Λ from the corresponding ones of A and B.

Citations

• Gorenstein defect categories of triangular matrix algebras
• The Gorenstein defect category

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• Gorenstein projective objects over cleft extensions

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