Dissertations, Theses, and Capstone Projects
Date of Degree
9-2024
Document Type
Dissertation
Degree Name
Ph.D.
Program
Mathematics
Advisor
Benjamin Steinberg
Committee Members
Alina Vdovina
Vladimir Shpilrain
Subject Categories
Algebra | Discrete Mathematics and Combinatorics | Dynamical Systems | Geometry and Topology
Keywords
etale groupoid algebra, Steinberg algebra, groupoid, Leavitt path algebra, inverse semigroup algebra, chain conditions, semisimplicity, associative ring
Abstract
Let R be a unital commutative ring and G an ample groupoid. Using the topology of the groupoid G, Steinberg defined an étale groupoid algebra RG. These étale groupoid algebras generalize various algebras, including group algebras, commutative algebras over a field generated by idempotents, traditional groupoid algebras, Leavitt path algebras, higher-rank graph algebras, and inverse semigroup algebras. Steinberg later characterized the classical chain conditions for étale groupoid algebras. In this work, we characterize categorically noetherian and artinian, locally noetherian and artinian, and semisimple étale groupoid algebras, thereby generalizing existing results for Leavitt path algebras and introducing new results for inverse semigroup algebras.
Recommended Citation
Philip, Sunil, "Categorical Chain Conditions for Étale Groupoid Algebras" (2024). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/6044
Included in
Algebra Commons, Discrete Mathematics and Combinatorics Commons, Dynamical Systems Commons, Geometry and Topology Commons