In [2], we considered a class of Lie algebras generalizing the classical simple Lie algebras. Using a field Φ of characteristic zero and a square matrix (Aij ) of integers with the properties (1) Aii = 2, (2) Aij ≦ 0 if i ≠ j, (3) Aij = 0 if and only if Ajt = 0, and (4) is symmetric for some appropriate non-zero rational a Lie algebra E = E((Aij)) over Φ can be constructed, together with the usual accoutrements: a root system, invariant bilinear form, and Weyl group.For indecomposable (A ij), E is simple except when (Aij) is singular and removal of any row and corresponding column of (Aij) leaves a Cartan matrix. The non-simple Es, Euclidean Lie algebras, were our object of study in [3] as well as in the present paper. They are infinite-dimensional, have ascending chain condition on ideals, and proper ideals are of finite codimension.
Moody, Robert V. Simple Quotients of Euclidean Lie Algebras. Canadian journal of mathematics, Tome 22 (1970) no. 4, pp. 839-846. doi: 10.4153/CJM-1970-095-3
@article{10_4153_CJM_1970_095_3,
author = {Moody, Robert V.},
title = {Simple {Quotients} of {Euclidean} {Lie} {Algebras}},
journal = {Canadian journal of mathematics},
pages = {839--846},
year = {1970},
volume = {22},
number = {4},
doi = {10.4153/CJM-1970-095-3},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1970-095-3/}
}
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