The Isomorphism Problem for Universal Enveloping Algebras of Lie Algebras

被引：0
|
作者：
David Riley
Hamid Usefi
机构：
[1] The University of Western Ontario,Department of Mathematics
来源：
Algebras and Representation Theory | 2007年 / 10卷
关键词：
Universal enveloping algebras; Lie algebras; Primary 17B35; Secondary 16R10; 17B01; 20C05;
D O I：
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学科分类号：
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) ≅ 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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