Coisotropic Subalgebras of Complex Semisimple Lie Bialgebras

Given a complex, semisimple Lie biaglebra, we consider the coisotropic subalgebras--the Lie subalgebras of whose annihilator in the dual space is a Lie subalgebra of the dual space. M. Zambon gives a construction for certain coisotropic sugalgebras, he explains his construction explicitly for the classical simple Lie algebras. In this dissertation, we explicitly compute Zambon's coisotroic subalgebras for a general complex semisimple Lie algebra and show that these coisotropic subalgebaras are a special case of a more general construction. Furthermore, we view coisotropic subalgebras of inside the variety of Lagrangian subalgebras of the double.