Dissertations, Theses, and Capstone Projects
Date of Degree
6-2026
Document Type
Doctoral Dissertation
Degree Name
Doctor of Philosophy
Program
Mathematics
Advisor
Benjamin Steinberg
Committee Members
Benjamin Steinberg
Olga Kharlampovich
Alina Vdovina
Subject Categories
Algebra | Discrete Mathematics and Combinatorics | Harmonic Analysis and Representation | Mathematics | Other Mathematics
Keywords
Quiver, Basic algebra, AFFINE MONOID, ADMISSBLE IDEAL, SEMIGROUP
Abstract
In this paper, we study the quiver of the complex monoid algebra CAFF(n, q). There are n + 1 maximal subgroups of AFF(n, q), each isomorphic to AGL(k, q) for some 0 ≤ k ≤ n. Every irreducible representation of CAFF(n, q) arises from a character of CAGL(k, q) for a suitable k. Thus, we study two different approaches to classifying the characters of CAGL(k, q). Next, we compute the full quiver Q(CAFF(n, q)). Finally, we show that this quiver is a disjoint union of straight-line paths and that its basic algebra has radical square zero. Hence, it has finite representation type.
Recommended Citation
Cleary, James Junie Chen, "Quiver of Affine Monoid of a Vector Space Over Finite Field" (2026). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/6647
Included in
Algebra Commons, Discrete Mathematics and Combinatorics Commons, Harmonic Analysis and Representation Commons, Other Mathematics Commons
