The Isomorphy Classes of the Special Orthogonal Group of Low Dimension in Characteristic 2
Session Number
Project ID: MATH 02
Advisor(s)
Dr. Ellen Ziliak; Benedictine University
Discipline
Mathematics
Start Date
19-4-2023 11:25 AM
End Date
19-4-2023 11:50 AM
Abstract
In 1926, Cartan introduced the concept of real symmetric spaces as a class of homogeneous Riemannian manifolds, where a symmetric space is defined as the homogeneous space $G/H$ with $G$ a reductive group and $H=G^{\theta}=\{g\in G|\theta(g)=g\}$, the fixed-point group of an $n$-automorphism. Of special interest are automorphism of order 2, also called involutions. In this project we focused on classifying the involutions for the $SO(3,\mathbb{F}_{2^k})$ and $SO(4,\mathbb{F}_{2^k})$. Our results should provide a base case for the general theory for n-dimensional matrices.
Note: The above math text can be compiled using LaTeX.
The Isomorphy Classes of the Special Orthogonal Group of Low Dimension in Characteristic 2
In 1926, Cartan introduced the concept of real symmetric spaces as a class of homogeneous Riemannian manifolds, where a symmetric space is defined as the homogeneous space $G/H$ with $G$ a reductive group and $H=G^{\theta}=\{g\in G|\theta(g)=g\}$, the fixed-point group of an $n$-automorphism. Of special interest are automorphism of order 2, also called involutions. In this project we focused on classifying the involutions for the $SO(3,\mathbb{F}_{2^k})$ and $SO(4,\mathbb{F}_{2^k})$. Our results should provide a base case for the general theory for n-dimensional matrices.
Note: The above math text can be compiled using LaTeX.