Graded subalgebras associated with a subalgebra of a graded free lie algebra

Non-degenerate graded Lie algebras with a degenerate transitive subalgebra

The property of degeneration of modular graded Lie algebras, first investigated by B. Weisfeiler, is analyzed. Transitive irreducible graded Lie algebras L = ∑ i∈Z Li, over algebraically closed fields of characteristic p > 2, with classical reductive component L0 are considered. We show that if a non-degenerate Lie algebra L contains a transitive degenerate subalgebra L′ such that dimL1 > 1, th...

Differential Graded Algebra

Differential Graded Algebra

When Does the Associated Graded Lie Algebra of an Arrangement Group Decompose?

Let A be a complex hyperplane arrangement, with fundamental group G and holonomy Lie algebra H. Suppose H3 is a free abelian group of minimum possible rank, given the values the Möbius function μ : L2 → Z takes on the rank 2 flats of A. Then the associated graded Lie algebra of G decomposes (in degrees ≥ 2) as a direct product of free Lie algebras. In particular, the ranks of the lower central ...

Graded Simple Lie Algebras and Graded Simple Representations

For any finitely generated abelian group Q, we reduce the problem of classification of Q-graded simple Lie algebras over an algebraically closed field of “good” characteristic to the problem of classification of gradings on simple Lie algebras. In particular, we obtain the full classification of finite-dimensional Q-graded simple Lie algebras over any algebraically closed field of characteristi...