Date of Publication

2026

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics with specialization in Business Applications

Subject Categories

Algebra | Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics Department

Thesis Advisor

Rafael Reno S. Cantuba

Defense Panel Chair

John Vincent S. Morales

Defense Panel Member

Jose Tristan F. Reyes

Abstract (English)

In this paper, we study a nonassociative and noncommutative algebraic structure in C[S3], which is that of a Lie algebra, with the commutator as the Lie bracket. By using properties of nested commutators, we exhibit a Lie subalgebra of C[S3] isomorphic to the Lie algebra so(3). We show that C[S3] can be decomposed into the direct sum of its center and the Lie subalgebra isomorphic to so(3). Another result is on the characterization of the Lie polynomials in C[S3] generated by A and B, which are generators of C[S3] under a well-known presentation of S3.

Abstract Format

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Abstract (Filipino)

Sa papel na ito, inaaral ang mga estrukturang nonassociative at noncommutative algebraic sa C[S3], estruktura ng isang Lie algebra, kung saan ang Lie bracket ay ang karaniwang commutator. Sa pamamagitan ng paggamit ng mga katangian ng mga nested commutators, ineeksibit ang Lie subalgebra ng C[S3] na isomorphic sa Lie algebra so(3). Ipinapakita na ang C[S3] ay maaaring ihiwalay sa direct sum ng kanyang center at ang Lie subalgebra na isomorphic sa so(3). Isa pang resulta ay sa characterization ng mga Lie polynomials sa C[S3] na binubuo ng A and B, na siyang mga generators ng C[S3] sa ilalim ng isang well-known presentation ng S3.

Abstract Format

html

Language

English

Format

Electronic

Keywords

Lie algebras; Group algebras; Symmetry groups

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Embargo Period

4-17-2026

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