On central extensions of preprojective algebras

被引：1
|
作者：
Etingof, Pavel
Latour, Frederic
Rains, Eric
机构：
[1] MIT, Dept Math, Cambridge, MA 02139 USA
[2] Cent Connecticut State Univ, Dept Math, New Britain, CT 06050 USA
[3] Univ Calif Davis, Davis, CA 95616 USA
来源：
JOURNAL OF ALGEBRA | 2007年 / 313卷 / 01期
基金：
美国国家科学基金会;
关键词：
preprojective algebra; simple Lie algebra; quiver;
D O I：
10.1016/j.jalgebra.2006.11.040
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that the Hilbert polynomial P(t) of the trace space A/[A, A] of the centrally extended preprojective algebra A of an ADE quiver is equal to the Hilbert series of the maximal nilpotent subalgebra of the corresponding simple Lie algebra under the principal gradation. This implies that the Hilbert polynomial of the center of A is t(2h-4p)(1/t), where It is the Coxeter number. (c) 2007 Elsevier Inc. All rights reserved.
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页码：165 / 175
页数：11
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