Integral bases for the universal enveloping algebras of map algebras

被引：10
|
作者：
Chamberlin, Samuel [1 ]
机构：
[1] Park Univ, Dept Comp Sci Informat Syst & Math, Parkville, MO 64152 USA
来源：
JOURNAL OF ALGEBRA | 2013年 / 377卷
关键词：
Lie algebras; Integral forms; Integral bases; Map algebras; Straightening identity; FINITE-DIMENSIONAL REPRESENTATIONS; LOOP ALGEBRAS;
D O I：
10.1016/j.jalgebra.2012.11.046
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Given a finite-dimensional, simple Lie algebra g over C and A, a commutative, associative algebra with unity over C, we exhibit an integral form for the universal enveloping algebra of the map algebra, U(g circle times A), and an explicit Z-basis for this integral form. We also produce explicit commutation formulas in the universal enveloping algebra of sl(2) circle times A that allow us to write certain elements in Poincare-Birkhoff-Witt order. (C) 2012 Elsevier Inc. All rights reserved.
引用
收藏
页码：232 / 249
页数：18
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