that g* has the same derived algebra as g itself and that every ideal in g is also an ideal in t*. Let g be any algebraic Lie algebra. Denote by b the radical of g (i.e., the largest solvable ideal in g) and by n the largest ideal of g composed only of nilpotent matrices. By Levi's theorem, g is the direct sum of t and of a semi-simple subalgebra J. It can be proved that f is the direct sum of ...

We compare the maximal dimension of abelian subalgebras and the maximal dimension of abelian ideals for finite-dimensional Lie algebras. We show that these dimensions coincide for solvable Lie algebras over an algebraically closed field of characteristic zero. We compute this invariant for all complex nilpotent Lie algebras of dimension n ≤ 7. Furthermore we study the case where there exists an...

In this paper we establish the correspondence between Bogoyavlenskij symmetries [1, 2] of the MHD equilibrium equations and Lie point transformations of these equations. We show that certain non-trivial Lie point transformations (that are obtained by direct application of Lie method) are equivalent to Bogoyavlenskij symmetries. PACS Codes: 05.45.-a , 02.30.Jr, 02.90.+p, 52.30.Cv.

The Joseph ideal is a special ideal in the universal enveloping algebra of a simple Lie algebra. For the classical groups, its uniqueness is equivalent to the existence of tensors with special properties. The existence of these tensors is usually concluded abstractly but here we present explicit formulae. This allows a rather direct computation of a parameter used in defining the Joseph ideal.

Let A be a graded-commutative, connected k-algebra generated in degree 1. The homotopy Lie algebra gA is defined to be the Lie algebra of primitives of the Yoneda algebra, ExtA(k, k). Under certain homological assumptions on A and its quadratic closure, we express gA as a semi-direct product of the well-understood holonomy Lie algebra hA with a certain hA-module. This allows us to compute the h...