Notes on the Hochschild homology dimension and truncated cycles

被引：0

作者：

Itagaki, Tomohiro ^{[1
]}

Sanada, Katsunori ^{[1
]}

机构：

[1] Tokyo Univ Sci, Dept Math, Shinjuku Ku, Tokyo 1628601, Japan

来源：

ARCHIV DER MATHEMATIK | 2014年 / 103卷 / 03期

关键词：

Hochschild homology dimension; Truncated cycle; No loops conjecture; QUADRATIC MONOMIAL ALGEBRAS; QUIVER ALGEBRAS; COHOMOLOGY; CONJECTURE;

D O I：

10.1007/s00013-014-0683-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we show that if an algebra KQ/I with an ideal I of KQ contained in for an integer m a parts per thousand yen 2 has an m-truncated cycle, then this algebra has infinitely many nonzero Hochschild homology groups, where R (Q) denotes the arrow ideal. Consequently, such an algebra of finite global dimension has no m-truncated cycles and satisfies an m-truncated cycles version of the "no loops conjecture".

引用

页码：219 / 228

页数：10

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