Date of Publication

3-2025

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Subject Categories

Physical Sciences and Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics Department

Thesis Advisor

John Vincent S. Morales

Defense Panel Chair

Arlene A. Pascasio

Defense Panel Member

Jose Maria P. Balmaceda
Diana C. Songsong
Rafael Reno S. Cantuba
Tessie M. Palma

Abstract/Summary

Let 𝔽 denote an algebraically closed field with characteristic 0. One of the well-studied Lie algebras over 𝔽 is the special linear algebra π–˜π–‘2 which has a Chevalley basis {e,h,f}. Since the special orthogonal algebra π–˜π–”4 is the Lie algebra over 𝔽 isomorphic to π–˜π–‘2β¨π–˜π–‘2, π–˜π–”4 has a Chevalley basis {e1, h1, f1, e2, h2, f2}. In 2022, J. Morales found an automorphism *:π–˜π–”4β†’π–˜π–”4 using some parameters p1,p2βˆˆπ”½ such that p1,p2βˆ‰{0,1}. By this automorphism, he found another Chevalley basis {e1*,h1*,f1*,e2*,h2*,f2*} of π–˜π–”4. He also described a simple construction of a finite-dimensional irreducible π–˜π–”4-module V in which π–˜π–”4 acts by derivation. In this paper, we construct four tridiagonal pairs on V via the actions of the Chevalley bases of π–˜π–”4. We show that these tridiagonal pairs are of Krawtchouk type and that the isomorphism of these tridiagonal pairs depends on the parameters p1 and p2. Consequently, we display four Lie algebra homomorphisms from the tetrahedron algebra ⊠ to π–˜π–”4 and via these homomorphisms, we describe how the generators of ⊠ act on V. Finally, we show that the irreducible π–˜π–”4-module V is isomorphic to a tensor product of two evaluation modules.

Abstract Format

html

Language

English

Format

Electronic

Keywords

Lie algebras

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Embargo Period

4-14-2025

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