Let U denote the enveloping algebra of the simple Lie algebra ~42, C). In this paper it is shown that the Krull dimension of U (denoted ] U]) is two. If U(g) is the enveloping algebra of a finite-dimensional solvable Lie algebra g then it is straightforward to show that ) U(g)] = dim g [5, 3.8.111. The problem as to the Krull dimension of U was first mentioned by Gabriel and Nouazt [9] they sho...

For any field F , we give an example of a prime finitely generated F -algebra of GK dimension 2 for which GK dimension is not finitely partitive. For each m ∈ {0, 1, 2, 3, . . .}∪{∞}, we give an example of a prime finitely generated F -algebra having GK dimension 2 which has classical Krull dimension m; the algebra of GK dimension 2 which has infinite classical Krull dimension has the additiona...