In this thesis, we will explore the structure of Terwilliger algebras over several different types of finite groups. We will begin by discussing what a Schur ring is, as well as providing many different results and examples of them. Following our discussion on Schur rings, we will move onto discussing association schemes as well as their properties. In particular, we will show every Schur ring gives rise to an association scheme. We will then define a Terwilliger algebra for any finite set, as well as discuss basic properties that hold for all Terwilliger algebras. After specializing to the case of Terwilliger algebras resulting from the orbits of a group, we will explore bounds of the dimension of such a Terwilliger algebra. We will also discuss the Wedderburn decomposition of a Terwilliger algebra resulting from the conjugacy classes of a group for any finite abelian group and any dihedral group.
College and Department
Physical and Mathematical Sciences
BYU ScholarsArchive Citation
Bastian, Nicholas Lee, "Terwilliger Algebras for Several Finite Groups" (2021). Theses and Dissertations. 8897.
Terwilliger algebra, Wedderburn decomposition, association scheme, Bose-Mesner algebra, Schur ring, representation theory, dihedral groups