{"id":{"repo_id":"wfu","oai_identifier":"oai:wakespace.lib.wfu.edu:10339/59320"},"canonical_url":"https://search.dev.ndltd.org/etd/wfu/oai:wakespace.lib.wfu.edu:10339/59320","repository":{"repo_id":"wfu","name":"Wake Forest University","base_url":"https://wakespace.lib.wfu.edu/oai/request"},"display":{"title":"Dual Reflection Groups of Low Order","abstract":"We consider group-gradings of noncommutative algebras with the following question in mind: for what groups $G$ does there exist an Artin-Schelter regular algebra $A$ with $G$ grading $A$ such that $A_e$, the identity-graded component of $A$, is itself Artin-Schelter regular? And in particular, restricting further, what if we require $A$ to be a quadratic domain? Results exist regarding the Poincar\\'e polynomial of a group with respect to an arbitrary generating set that grades an Artin-Schelter regular algebra in this way, which we use to narrow down possible grades of the generators of $A$.","abstract_html":"We consider group-gradings of noncommutative algebras with the following question in mind: for what groups $G$ does there exist an Artin-Schelter regular algebra $A$ with $G$ grading $A$ such that <span class=\"etd-inline-math\">A<sub>e</sub></span>, the identity-graded component of $A$, is itself Artin-Schelter regular? And in particular, restricting further, what if we require $A$ to be a quadratic domain? Results exist regarding the Poincar\\&#x27;e polynomial of a group with respect to an arbitrary generating set that grades an Artin-Schelter regular algebra in this way, which we use to narrow down possible grades of the generators of $A$.","abstract_has_math":true,"creators":["Vashaw, Kent Barton"],"institution":"Wake Forest University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016","date_published":"2016","updated_at":"2026-07-27T22:02:05Z","subjects":["Algebra"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10339/59320","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Vashaw, Kent Barton"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-05-21T08:35:52Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-05-21T08:35:52Z"]},{"key":"dc:date.issued","label":"Date","values":["2016"]},{"key":"dc:publisher","label":"Institution","values":["Wake Forest University"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Algebra"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10339/59320"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We consider group-gradings of noncommutative algebras with the following question in mind: for what groups $G$ does there exist an Artin-Schelter regular algebra $A$ with $G$ grading $A$ such that $A_e$, the identity-graded component of $A$, is itself Artin-Schelter regular? And in particular, restricting further, what if we require $A$ to be a quadratic domain? Results exist regarding the Poincar\\'e polynomial of a group with respect to an arbitrary generating set that grades an Artin-Schelter regular algebra in this way, which we use to narrow down possible grades of the generators of $A$."]},{"key":"dc:title","label":"Title","values":["Dual Reflection Groups of Low Order"]}]}],"canonical_facts":{"dc:creator":["Vashaw, Kent Barton"],"dc:date.accessioned":["2016-05-21T08:35:52Z"],"dc:date.available":["2016-05-21T08:35:52Z"],"dc:date.issued":["2016"],"dc:description.abstract":["We consider group-gradings of noncommutative algebras with the following question in mind: for what groups $G$ does there exist an Artin-Schelter regular algebra $A$ with $G$ grading $A$ such that $A_e$, the identity-graded component of $A$, is itself Artin-Schelter regular? And in particular, restricting further, what if we require $A$ to be a quadratic domain? Results exist regarding the Poincar\\'e polynomial of a group with respect to an arbitrary generating set that grades an Artin-Schelter regular algebra in this way, which we use to narrow down possible grades of the generators of $A$."],"dc:identifier.uri":["http://hdl.handle.net/10339/59320"],"dc:language.iso":["en"],"dc:publisher":["Wake Forest University"],"dc:subject":["Algebra"],"dc:title":["Dual Reflection Groups of Low Order"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T22:02:05Z"}