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.

引用

页码：517 / 532

页数：16

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