Seaweed algebras (``seaweeds'') are certain Lie subalgebras of the complex simple Lie algebras which are defined in terms of their attendant root systems. We review this setup and show, as a corollary to a strong cohomology result, that if $\mathfrak{s}$ is an indecomposable (not a direct sum) seaweed then $\mathfrak{s}$ is absolutely rigid. However, decomposable seaweeds can have non-trivial cohomology and may deform; examples are given.

In characteristic $p$, the situation is more complicated since simple modular Lie algebras need not have root systems; those that do give rise to \textit{modular seaweeds} in a natural way.

The cohomology of indecomposable modular seaweeds with coefficients in the adjoint representation is zero, as in the characteristic zero case -- so long as the rank of the modular seaweed is sufficiently larger the rank of the seaweed.