Title: Lie Algebras and Geometric Structures for Undergraduates

Directors:

- Gueo Grantcharov
- Mirroslav Yotov

Email:

Dates of Program: May 9 - June 17, 2011

Summary:

This proposed project will study a relation between Linear Algebra and Graph Theory with a view toward Differential Geometric applications. In 2004, S. Dani and M. Miankar associated to a directed graph a two-step nilpotent Lie algebra in a pretty easy way: For any such graph with vertices *V* = {*v _{1}, . . . , v_{n}*} and edges

[

if

M. Miankar proved recently that two such 2-step nilpotent Lie algebras are isomorphic iff their corresponding graphs are isomorphic. The students participating in the project will explore further the construction above concentrating on two main problems. The first one is about extending the categorical properties of the relation beyond the statement above. A natural question here is whether there is an additional category structure on the set of graphs for which the correspondence is a functor into the category of Lie algebras. Also how to characterize the algebras corresponding to particular types of graphs, such as bipartite, Eulerian, Hamiltonian,

Student Researchers Supported by MAA:

- Lazaro Diaz
- Omar Jesus Leon
- Alexander Moncion
- Austin Nowak

More Information: www2.fiu.edu/~sumres11/home.html

Program Contacts:

Bill Hawkins

MAA SUMMA

bhawkins@maa.org

202-319-8473

Michael Pearson

MAA Programs & Services

pearson@maa.org

202-319-8470