Representation dimension of artin algebras
Representation dimension of artin algebras
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DOI：
10.11606/issn.2316-9028.v4i3p479-498
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发表时间：
2010-12
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影响因子：
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通讯作者：
Steffen Oppermann
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文献类型：
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作者：
Steffen Oppermann
Auslander证明了一个代数是有限表示型的，也就是说，它只允许有1000个不可分解模直到同构，当且仅当它的表示维数至多为2。我们将在第1节中作为推论1.9给出这一事实的证明。这导致Auslander的期望，“这一概念给出了一个合理的方式来衡量多远的artin代数是从有限的代表性类型。”[第一、三.5段，第2、3行]
Auslander has shown that an algebra is of finite representation type, that is, it admits only finitely many indecomposable modules up to isomorphism, if and only if its representation dimension is at most 2. We will give a proof of this fact in Section 1 as Corollary 1.9. This led Auslander to the expectation, “that this notion gives a reasonable way of measuring how far an artin algebra is from being of finite representation type.” [1, III.5, lines 2, 3]