The isomorphism problem for universal enveloping algebras of lie algebras

被引：11
|
作者：
Riley, David [1 ]
Usefi, Hamid [1 ]
机构：
[1] Univ Western Ontario, Dept Math, London, ON N6A 5B7, Canada
来源：
ALGEBRAS AND REPRESENTATION THEORY | 2007年 / 10卷 / 06期
基金：
加拿大自然科学与工程研究理事会;
关键词：
universal enveloping algebras; lie algebras;
D O I：
10.1007/s10468-007-9083-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let L be a Lie algebra with universal enveloping algebra U(L). We prove that if H is another Lie algebra with the property that U(L) congruent to U(H) then certain invariants of L are inherited by H. For example, we prove that if L is nilpotent then H is nilpotent with the same class as L. We also prove that if L is nilpotent of class at most two then L is isomorphic to H.
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页码：517 / 532
页数：16
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