ICE-closed subcategories and epibricks over one-point extensions

2024/01/11 by Li, Xin, Gao, Hanpeng · 1 citation
#16G20 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2401.05645

Abstract

Let B be the one-point extension algebra of A by an A-module M. We proved that every ICE-closed subcategory in\mod A can be extended to be some ICE-closed subcategories in\mod B.In the same way, every epibrick in \mod A can be extended to be some epibricks in \mod B.The number of ICE-closed subcategories in \mod B and the number of ICE-closed subcategories in \mod A are denoted respectively as m, n.We can conclude the following inequality:m ≥ 2n This is the analogical in epibricks.As an application, we can get some wide τ-tilting modules of B by wide τ-tilting modules of A.

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• On bricks of one-point extension algebras

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