Graduation Term
Spring 2025
Degree Name
Master of Science (MS)
Department
Department of Mathematics
Committee Chair
Gaywalee Yamskulna
Committee Member
Charlotte Ure
Abstract
A fundamental problem in the study of vertex (operator) algebras V is the determination of the group of (grading-preserving) N-graded vertex algebras associated with cyclic Leibniz algebras of dimensions 2 and 3 that were classified by C. Barnes, E. Martin, J. Service, and G. Yamskulna in [1].
In each case examined, investigation of the automorphism group relies on the key fact that the action of an automorphism σ is determined solely by its value at a single basis element b. Furthermore, we employ a result in [19] by H. Li and G. Yamskulna which states that we can determine the automorphism groups of these N-graded vertex algebras in terms of the automorphism groups of the corresponding vertex algebroids.
Access Type
Thesis-Open Access
Recommended Citation
Keene, Alexander M., "Automorphism Groups of N-Graded Vertex Algebras associated with Cyclic Leibniz Algebras with Small Dimensions" (2025). Theses and Dissertations. 2085.
https://ir.library.illinoisstate.edu/etd/2085