On the Coisotropic Subalgebras of a Complex Semisimple Lie Algebra

Given a complex semisimple Lie bialgebra g, a Lie subalgebra c of g is coisotropic if the annihilator of c in g^* is a Lie subalgebra of g^*. Kroeger shows in her paper that coisotropic subalgebras give rise to Lagrangian subalgebras of g+g. By studying the Lagrangian subalgebras of g+g, she generalizes Zambon's work by constructing a more general class of isolated coisotropic subalgebras in g.

Motivated by Kroeger's method of studying coisotropic subalgebras, in this dissertation, we classify coisotropic subalgebras in the subset L_{G} of the Lagrangian subalgebras of g+g. These are the first examples of non-isolated coisotropic subalgebras.

We also give the complete list of coisotropic subalgebras in the sl(2,C) case. Lastly, we study the Lagrangian subalgebras of the standard parabolic subalgebras and produce a class of coisotropic subalgebras. The result generalizes a basic theorem of Kroeger.