Lie polynomial characterization in a q-deformed universal enveloping algebra of a low-dimensional Lie algebra

Author

Mark Anthony C. Merciales, De La Salle University, ManilaFollow

Date of Publication

7-2025

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Subject Categories

Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics Department

Thesis Advisor

Rafael Reno S. Cantuba

Defense Panel Chair

Arlene A. Pascasio

Defense Panel Member

Kai Brynne M. Boydon-Ong
Edmundo R. Perez, Jr
John Vincent S. Morales
Daryl Q. Granario

Abstract (English)

Let k be a field, and fix q, r, s in k. Let U_q(r, s) denote the associative algebra generated by two elements A, B that satisfy the relation AB-qBA=rA+sB. We give U_q(r, s) a presentation in three generators by introducing C=[A,B]:=AB-BA. We employ Bergman's Diamond Lemma to construct a basis for the algebra U_q(r, s), which simultaneously serves as a basis for the two generalized q-deformed universal enveloping algebras of two-dimensional Lie algebras generated by A and B, defined respectively by the relations AB-qBA=rA and AB-qBA=sB. Furthermore, we determine a solution to the Lie polynomial characterization problem in the corresponding class of q-deformed universal enveloping algebras.

Abstract Format

html

Abstract (Filipino)

N/A

Abstract Format

html

Language

English

Format

Electronic

Keywords

Lie algebras; Universal enveloping algebras

Recommended Citation

Merciales, M. C. (2025). Lie polynomial characterization in a q-deformed universal enveloping algebra of a low-dimensional Lie algebra. Retrieved from https://animorepository.dlsu.edu.ph/etdd_math/6

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Embargo Period

12-10-2025