Orthogonal Abelian Cartan Subalgebra Decompositions of Classical Lie Algebras Over Finite Commutative Rings

Songpon Sriwongsa
University of Wisconsin-Milwaukee
PhD Graduate Student

“Orthogonal decompositions of classical Lie algebras over the complex numbers of types A, B, C and D were studied in the early 1980s and attracted further attention in the past decade, especially in the type A case, due to its application in quantum information theory.
In this dissertation, we consider the orthogonal decomposition problem of Lie algebras of type A, B, C and D over a finite commutative ring with identity. Our goal is to construct interesting orthogonal decompositions of these Lie algebras. We begin with Lie algebras of type A by searching for sufficient conditions for the existence of such an orthogonal decomposition. We then apply our results on the orthogonal decomposition of type A Lie algebras to obtain a construction of the orthogonal decomposition of Lie algebras of type C. We also provide methods of constructing orthogonal decompositions for Lie algebras of types B and D.”

Committee Members:
Profs. Yi Ming Zou (Advisor); Allen Bell, Craig Guilbault, Kevin McLeod &  Jeb Willenbring