Date of Publication

5-2012

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Subject Categories

Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics Department

Thesis Adviser

Arlene A. Pascasio

Defense Panel Chair

Ederlina G. Nocon

Defense Panel Member

Isagani B. Jos
Edmundo R. Perez

Abstract/Summary

Let QD denote the graph of the D-dimensional hypercube where D is a positive integer. Let X denote the vertex set of QD. Let MatX(C) denote the C-algebra of matrices with entries in C and whose rows and columns are indexed by X. Let A denote the adjacency matrix of QD and let 0 > 1 > > D denote the eigenvalues of A. Fix a vertex x 2 X. For 0 i D, let Ei (resp. E i = E i (x)) denote the primitive idempotent (ith dual idempotent with respect to x) of QD. Let A = A (x) denote the dual adjacency matrix of QD and let 0 > 1 > > D denote the dual eigenvalues of A . Let V = CX. For 0 i D, we de ne Ui := (E 0V + E 1V + + E i V ) \ (EiV + Ei+1V + + EDV ) where EiV (resp. E i V ) is the eigenspace associated with the eigenvalue i (resp. dual eigenvalue i ). We show that V = U0 + U1 + + UD (direct sum). We give a basis for Ui (0 i D). We give the action of A and A on this basis. We de ne B := A + A 1 2 (AA A A). We show that for 0 i D, Ui is the eigenspace of B associated with the eigenvalue i. We display a Lie algebra isomorphism from a Lie subalgebra of MatX(C) to sl2(C), where sl2(C) denotes the Lie subalgebra of Mat2(C) consisting of 2 2 matrices whose trace is 0. Using this, we display an action of the tetrahedron Lie algebra on V.

Abstract Format

html

Language

English

Format

Electronic

Electronic File Format

MS WORD

Accession Number

TG05113

Shelf Location

Archives, The Learning Commons, 12F Henry Sy Sr. Hall

Physical Description

63 leaves : ill. ; 1 computer optical disc

Keywords

Algebra; Hypercube

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