Date of Award
Master of Science (MS)
Department of Mathematics
The notion of vertex algebroids were introduced in the late 1990's as a crucial tool for the study of chiral differential operators and chiral de Rham complex. Vertex algebroids play vital role in the study of N-graded vertex algebra. Also, they have deep connection with representation theory of Leibniz algebras. However, the classification of irreducible modules of vertex algebroids is not completed.
The aim of this thesis is to investigate the possibility of using the simple Lie algebra G_2 and its irreducible modules to construct vertex A-algebroids B that contain G_2 as their Levi factor. Under very mild and natural assumptions, I find some exact properties on the algebraic structure of A and B that will provide precise algebraic structure of the vertex A-algebroid B.
Klecki, Nicholas J., "Towards Constructing Vertex Algebroids" (2021). Theses and Dissertations. 1383.