Lie algebras graded by the weight system (Θn,sln)

Abstract

Abstract A Lie algebra L is said to be ( Θ n , sl n ) -graded if it contains a simple subalgebra g isomorphic to s l n such that the g -module L decomposes into copies of the adjoint module, the trivial module, the natural module V, its symmetric and exterior squares S 2 V and ∧ 2 V and their duals. We describe the multiplicative structures and the coordinate algebras of ( Θ n , sl n ) -graded Lie algebras for n ≥ 5 , classify these Lie algebras and determine their central extensions.