  A Lie algebra $L$ is said to be $(\Theta_{n},sl_{n})$-graded if it contains a
simple subalgebra $\mathfrak{g}$ isomorphic to $sl_{n}$ such that the
$\mathfrak{g}$-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 $\wedge^{2}V$ and their duals. We describe the multiplicative
structures and the coordinate algebras of $(\Theta_{n},sl_{n})$-graded Lie
algebras for $n\ge5$, classify these Lie algebras and determine their central
extensions.
