Dr. Habermas' Group Project Information
"Lie groups, Lie algebras, and symmetric spaces"
A symmetric space is a Riemmanian manifold that has interesting geometric and algebraic
properties that make it convenient in modeling. One way of studying these spaces is to
study its group of isometries, transformations of the space that preserve its geometric
structure. This group is a Lie group, and a carefully chosen factorization of the
corresponding Lie algebra leads to a decomposition of the symmetric space important
in Poisson geometry. We will investigate this decomposition in low-dimensional symmetric
spaces, and use linear algebra techniques
to try to generate explicit formulas for the strata of this decomposition.
It will be assumed that students are comfortable working with cosets (for
example, in
an abstract algebra course). All other background will be picked up as
needed.
You can reach Dr. Habermas by email at habermds@potsdam.edu