rep(A3, I, A)中的Gorenstein投射模

罗秀花, 居腾霞, 吴美云

数学学报 ›› 2015, Vol. 58 ›› Issue (1) : 115-124.

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数学学报 ›› 2015, Vol. 58 ›› Issue (1) : 115-124. DOI: 10.12386/A2015sxxb0012
论文

rep(A3, I, A)中的Gorenstein投射模

    罗秀花, 居腾霞, 吴美云
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Gorenstein-Projective Modules in rep(A3, I, A)

    Xiu Hua LUO, Teng Xia JU, Mei Yun WU
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摘要

设A是域k上的有限维代数, (Q,I)是带关系的箭图,令Λ = A⊕kkQ/I.Λ的模范畴Λ-Mod及有限生成模范畴Λ-mod分别与(Q,I)在A上的表示范畴Rep(Q, I, A) 及有限维表示范畴rep(Q, I, A)等价. 给出了范畴rep(A3, I,A)中Gorenstein投射模的具体构造,其中(A3,I)=321,I=<βα>. 在此基础上,给出了代数A是自入射代数的一个充分必要条件.

Abstract

Given a finite-dimensional algebra A over a field k, and a quiver with relations (Q,I), let Λ = A⊕kkQ/I. The category Λ-Mod (Resp. Λ-mod) of (Resp. finitely generated) Λ-modules is equivalent to the category Rep(Q, I,A) (Resp. rep(Q, I,A)) of (Resp. finite-dimensional) representations of (Q, I) over A. The main result of this paper explicitly describes the Gorenstein-projective modules in rep(A3,I,A), where (A3, I) = 3 α 21. with relation I = < βα >. As a corollary, we give a necessary and sufficient condition for A being a self-injective algebra.

关键词

箭图在代数上的表示 / (强) Gorenstein投射模 / 自入射代数

Key words

representations of a quiver over an algebra / (strongly) Gorenstein-projective modules / self-injective algebras

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罗秀花, 居腾霞, 吴美云. rep(A3, I, A)中的Gorenstein投射模. 数学学报, 2015, 58(1): 115-124 https://doi.org/10.12386/A2015sxxb0012
Xiu Hua LUO, Teng Xia JU, Mei Yun WU. Gorenstein-Projective Modules in rep(A3, I, A). Acta Mathematica Sinica, Chinese Series, 2015, 58(1): 115-124 https://doi.org/10.12386/A2015sxxb0012

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基金

国家自然科学基金资助项目(11401323);南通大学引进人才科研启动费项目(13R40)

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