In this paper we introduce the definition of a reality-based algebra (RBA) as well as a subclass of reality-based algebras, table algebras. Using sesquilinear forms, we prove that a reality-based algebra is semisimple. We look at a specific reality-based algebra of dimension 5 and provide formulas for the structure constants of this algebra. We determine by looking at these structure constants and setting conditions on specific structural components when this particular reality-based algebra is a table algebra. In fact, this will be a noncommutative table algebra of dimension 5.
","abstract_html":"<p>In this paper we introduce the definition of a reality-based algebra (RBA) as well as a subclass of reality-based algebras, table algebras. Using sesquilinear forms, we prove that a reality-based algebra is semisimple. We look at a specific reality-based algebra of dimension 5 and provide formulas for the structure constants of this algebra. We determine by looking at these structure constants and setting conditions on specific structural components when this particular reality-based algebra is a table algebra. In fact, this will be a noncommutative table algebra of dimension 5. </p>","abstract_has_math":false,"creators":["Barber, Rachel Victoria"],"institution":"Eastern Kentucky University","degree_name":"Master of Science (MS)","degree_level":"Master's","degree_discipline":"Mathematics and Statistics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-01-01T08:00:00Z","date_published":"2016-01-01T08:00:00Z","updated_at":"2026-07-24T02:15:32Z","subjects":["adjacency","algebra","based","reality","sesquilinear","table"],"languages":[],"rights":["Copyright 2016 Rachel Victoria Barber"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://encompass.eku.edu/etd/336","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Barber, Rachel Victoria"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2016-10-25T07:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["Encompass Digital Archive, Eastern Kentucky University"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics and Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Master's"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MS)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Eastern Kentucky University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["adjacency","algebra","based","reality","sesquilinear","table"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2016 Rachel Victoria Barber"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://encompass.eku.edu/etd/336"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this paper we introduce the definition of a reality-based algebra (RBA) as well as a subclass of reality-based algebras, table algebras. Using sesquilinear forms, we prove that a reality-based algebra is semisimple. We look at a specific reality-based algebra of dimension 5 and provide formulas for the structure constants of this algebra. We determine by looking at these structure constants and setting conditions on specific structural components when this particular reality-based algebra is a table algebra. In fact, this will be a noncommutative table algebra of dimension 5.
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"],"dc:format":["application/pdf"],"dc:identifier":["https://encompass.eku.edu/etd/336"],"dc:publisher":["Encompass Digital Archive, Eastern Kentucky University"],"dc:rights":["Copyright 2016 Rachel Victoria Barber"],"dc:source":["Encompass Digital Archive: Online Theses and Dissertations"],"dc:subject":["adjacency","algebra","based","reality","sesquilinear","table"],"dc:title":["Low-Dimensional Reality-Based Algebras"],"dc:type":["Master Thesis"],"thesis:degree_discipline":["Mathematics and Statistics"],"thesis:degree_level":["Master's"],"thesis:degree_name":["Master of Science (MS)"],"thesis:institution_name":["Eastern Kentucky University"]},"updated_at":"2026-07-24T02:15:32Z"}