  We consider the universal central extension of the Lie algebra $\Vect
(S^1)${\math \s}$ C^{\infty}(S^1)$. The coadjoint representation of this Lie
algebra has a natural geometric interpretation by matrix analogues of the
Sturm-Liouville operators. This approach leads to new Lie superalgebras
generalizing the well-known Neveu-Schwartz algebra.
