Abstract
We make a detailed study of the Lie algebras , , of triangular polynomial derivations, their injective limit , and their completion . We classify the ideals of (all of which are characteristic ideals) and use this classification to give an explicit criterion for Lie factor algebras of and to be isomorphic. We introduce two new dimensions for (Lie) algebras and their modules: the central dimension and the uniserial dimension , and show that for all , where is the first infinite ordinal. Similar results are proved for the Lie algebras and . In particular, and .
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