On the Group of Transvections of ADE-Diagrams

Author

Marvin Jones, University of South Carolina - ColumbiaFollow

Date of Award

8-9-2014

Document Type

Open Access Thesis

Department

Mathematics

First Advisor

Jesse Kass

Abstract

In this thesis we examine symplectic spaces with forms generated by the ADEdiagrams. Specifically, we determine the generators of the group of transvections for each space under the standard basis, S, of Kⁿ (where K is a field with characteristic 0) and the hyperbolic basis, H, we get from the classification theorem of symplectic spaces. Further, we examine how the generators of these groups are related via g : G_f,S ! SL(Z)_n where g(X) = P⁻¹XP where P is the change of basis matrix for S to H.

Rights

© 2014, Marvin Jones

Recommended Citation

Jones, M.(2014). On the Group of Transvections of ADE-Diagrams. (Master's thesis). Retrieved from https://scholarcommons.sc.edu/etd/2842