2017/08/01 by Ming Lu, Bin Zhu, Lu, Ming +1 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.1708.00311
36 pages, some changes, to appear in JPAA
openalex publication_date 2017/08/01 · arxiv created 2020/12/12 · arxiv updated 2020/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider the singularity category Dsg(\mod A) and the ℤ-graded singularity category Dsg(\mod\mathbb Z A) for a Gorenstein monomial algebra A. Firstly, for a positively graded 1-Gorenstein algebra, we prove that its \mathbb Z-graded singularity category admits silting objects. Secondly, for A=KQ/I being a Gorenstein monomial algebra, we prove that Dsg(\mod\mathbb Z A) has tilting objects. As a consequence, Dsg(\mod\mathbb ZA) is triangulated equivalent to the derived category of a hereditary algebra H which is of finite representation type. Finally, we give a characterization of 1-Gorenstein monomial algebras, and describe their singularity categories clearly by using the triangulated orbit categories of type \mathbb A.