On Lie algebras associated with representation-directed algebras

被引：5

作者：

Kasjan, Stanislaw ^{[1
]}

Kosakowska, Justyna ^{[1
]}

机构：

[1] Nicolaus Copernicus Univ, Fac Math & Comp Sci, PL-87100 Torun, Poland

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2010年 / 214卷 / 05期

关键词：

HALL ALGEBRAS;

D O I：

10.1016/j.jpaa.2009.07.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let B be a representation-finite C-algebra. The Z-Lie algebra L(B) associated with B has been defined by Riedtmann in [Ch. Riedtmann, Lie algebras generated by indecomposables, J. Algebra 170 (1994) 526-546]. If B is representation-directed, there is another Z-Lie algebra associated with B defined by Ringel in [C.M. Ringel, Hall Algebras, vol. 26, Banach Center Publications, Warsaw, 1990, pp. 433-447] and denoted by K(B). We prove that the Lie algebras L(B) and K(B) are isomorphic for any representation-directed C-algebra B. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：678 / 688

页数：11

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