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Triangle Order ≤△ in Singular Categories

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Abstract

Degeneration of modules is defined geometrically. Riedtmann and Zwara show that this degeneration is equivalent to the existence of a certain short exact sequence. Then Yoshino and independently Jensen, Su and Zimmermann generalised this notion to triangulated categories. We write X≤Δ Y if X degenerates to Y. In this paper, we prove that ≤△ applied to the singular category \(\mathcal {D}_{\text {sg}}(A)\) of a finite-dimensional k-algebra A induces a partial order on the set of isomorphism classes of objects in \(\mathcal {D}_{\text {sg}}(A)\).

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Authors and Affiliations

  1. Université Paris Diderot-Paris 7, Institut de Mathématiques de Jussieu-Paris Rive Gauche CNRS UMR 7586, Bâtiment Sophie Germain, Case 7012, 75205, Paris Cedex 13, France

    Zhengfang Wang

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  1. Zhengfang Wang
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Correspondence to Zhengfang Wang.

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Presented by Michel Van den Bergh.

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Wang, Z. Triangle Order ≤△ in Singular Categories. Algebr Represent Theor 19, 397–404 (2016). https://doi.org/10.1007/s10468-015-9579-y

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  • DOI: https://doi.org/10.1007/s10468-015-9579-y

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