Term of Award
Summer 2025
Degree Name
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (open access)
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution 4.0 License.
Department
Department of Mathematical Sciences
Committee Chair
Dr. Paul Sobaje
Committee Member 1
Dr. Tricia Brown
Committee Member 2
Dr. Shijun Zheng
Abstract
We investigate whether there is an analog of the Baker-Campbell-Hausdorff (BCH) theorem for Lie algebras over fields of positive characteristic. We begin by introducing the proof of the BCH formula in characteristic zero. We then introduce the Artin-Hasse exponential and show that it is $p$-integral. Our main result provides sufficient conditions under which a BCH-type formula exists for the Artin-Hasse exponential in positive characteristic. Additionally, we derive a formula for computing an inverse of the Artin-Hasse exponential.
OCLC Number
1528900774
Catalog Permalink
https://galileo-georgiasouthern.primo.exlibrisgroup.com/permalink/01GALI_GASOUTH/1r4bu70/alma9916627634702950
Recommended Citation
Koutroulakis, Nikolas A., "Towards a Baker-Campbell-Hausdorff Theorem in Positive Characteristic" (2025). Theses & Dissertations. 2993.
https://digitalcommons.georgiasouthern.edu/etd/2993
Research Data and Supplementary Material
No
