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
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
Recommended Citation
Penaflor, R. A. (2012). The tetrahedron algebra and the hypercube. Retrieved from https://animorepository.dlsu.edu.ph/etd_doctoral/957
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