College of Arts and Sciences
Master of Science in Mathematical Sciences (MS)
Mathematics & Statistics
NACO controlled Corporate Body
University of North Florida. Department of Mathematics and Statistics
Dr. Jae-Ho Lee
Dr. Richard Patterson
We study the hypercube and the associated subconstituent algebra. Let Q_D denote the hypercube with dimension D and let X denote the vertex set of Q_D. Fix a vertex x in X. We denote by A the adjacency matrix of Q_D and by A* = A*(x) the diagonal matrix with yy-entry equal to D − 2i, where i is the distance between x and y. The subconstitutent algebra T = T(x) of Q_D with respect to x is generated by A and A* . We show that A 2A* − 2AA*A + A*A 2 = 4A* A*2A − 2A*AA* + AA*2 = 4A. Using these relations, we show that there exists a surjective C-algebra homomorphism from the universal enveloping algebra of the Lie algebra sl2(C) to T.
Billet, Jared B., "The Subconstituent Algebra of a Hypercube" (2020). UNF Graduate Theses and Dissertations. 945.