Graduation Year
2026
Date of Submission
4-2026
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Arts
Department
Mathematical Sciences
Reader 1
Robert Cass
Rights Information
© 2026 Hudson W Yeend
Abstract
Representation theory allows mathematicians to study abstract mathematical objects using the powerful and concrete tools of linear algebra. This thesis aims to present some foundational concepts in representation theory and apply these concepts to specific groups and algebras. We begin by examining representations of finite groups, culminating with a proof of Maschke's theorem. We then use the correspondence between a group and its group algebra to segue into a study of representations of diagrammatic algebras, where we introduce analogous notions of decomposition. We end with a study of quiver representations, noting that Gabriel's theorem and the kQ-modular structure transcend strictly algebraic applications.
Recommended Citation
Yeend, Hudson, "Representations of Finite Groups and Diagrammatic Algebras" (2026). CMC Senior Theses. 4116.
https://scholarship.claremont.edu/cmc_theses/4116
