Isomorphism theorem on low dimensional Lie algebras

Jang-Ho Chun, Takeshi Kajiwara and Jong-Sook Lee

Vol. 214 (2004), No. 1, 17–21

DOI: 10.2140/pjm.2004.214.17

Abstract

Let g (resp. g′) be a Lie algebra of dimension d ≤ 3 (resp. of finite dimension) over a field k of characteristic ≠2. We prove that g is isomorphic to g′ as Lie algebras over k if and only if the enveloping algebra U(g) of g is isomorphic to U(g′) as k-algebras.

Milestones

Received: 29 November 1999

Revised: 7 February 2003

Published: 1 March 2004