  We study the Lie module structure given by the Gerstenhaber bracket on the
Hochschild cohomology groups of a monomial algebra with radical square zero.
The description of such Lie module structure will be given in terms of the
combinatorics of the quiver. The Lie module structure will be related to the
classification of finite dimensional modules over simple Lie algebras when the
quiver is given by the two loops and the ground field is the complex numbers.
