The universal 2-parameter vertex algebra W∞ of type W(2, 3, 4; . . . ) serves as a classifying object for vertex algebras of type W(2, 3, . . . ,N) for some N in the sense that under mild hypothesis, all such vertex algebras arise as quotients of W∞. There is an ℕ X ℕ family of such 1-parameter vertex algebras known as Y-algebras. They were introduced by Gaiotto and Rapčák are expected to be building blocks for all W-algebras in type A, i.e, every W-(super) algebra in type A is an extension of a tensor product of finitely many Y-algebras. Similarly, the orthosymplectic Y-algebras are 1-parameter quotients of a universal 2-parameter vertex algebra of type W(2, 4, 6, . . . ), which is a classifying object for vertex algebras of type W(2, 4, . . . , 2N) for some N. Unlike type A, these algebras are not all the building blocks for W-algebras of types B, C, and D. In this thesis, we construct a new universal 2-parameter vertex algebra of type W(13, 2, 33, 4, 53, 6, . . . ) which we denote by W∞sp since it contains a copy of the affine vertex algebra Vk(sp2). We identify 8 infinite families of 1-parameter quotients W∞sp which are analogues of the Y-algebras, and 4 infinite families with sp2-level constant. We regard W∞sp as a fundamental object on equal footing with W∞ and W∞ev, and we give some heuristic reasons for why we expect the 1-parameter quotients of these three objects to be the building blocks for all W-algebras in classical types.
","abstract_html":"<p>The universal 2-parameter vertex algebra <em>W</em><sub>∞</sub> of type <em>W</em>(2, 3, 4; . . . ) serves as a classifying object for vertex algebras of type <em>W</em>(2, 3, . . . ,<em>N</em>) for some <em>N</em> in the sense that under mild hypothesis, all such vertex algebras arise as quotients of <em>W</em><sub>∞</sub>. There is an ℕ X ℕ family of such 1-parameter vertex algebras known as <em>Y</em>-algebras. They were introduced by Gaiotto and Rapčák are expected to be building blocks for all <em>W</em>-algebras in type<em> A</em>, i.e, every <em>W</em>-(super) algebra in type <em>A</em> is an extension of a tensor product of finitely many <em>Y</em>-algebras. Similarly, the orthosymplectic <em>Y</em>-algebras are 1-parameter quotients of a universal 2-parameter vertex algebra of type <em>W</em>(2, 4, 6, . . . ), which is a classifying object for vertex algebras of type <em>W</em>(2, 4, . . . , 2<em>N</em>) for some <em>N</em>. Unlike type <em>A</em>, these algebras are not all the building blocks for <em>W</em>-algebras of types <em>B</em>, <em>C</em>, and <em>D</em>. In this thesis, we construct a new universal 2-parameter vertex algebra of type <em>W</em>(1<sup>3</sup>, 2, 3<sup>3</sup>, 4, 5<sup>3</sup>, 6, . . . ) which we denote by <em>W<sub>∞</sub></em><sup>sp</sup> since it contains a copy of the affine vertex algebra <em>V<sup>k</sup></em>(sp<sub>2</sub>). We identify 8 infinite families of 1-parameter quotients <em>W<sub>∞</sub></em><sup>sp</sup> which are analogues of the <em>Y</em>-algebras, and 4 infinite families with sp<sub>2</sub>-level constant. We regard <em>W<sub>∞</sub></em><sup>sp</sup> as a fundamental object on equal footing with <em>W</em><sub>∞</sub> and <em>W<sub>∞</sub></em><sup>ev</sup>, and we give some heuristic reasons for why we expect the 1-parameter quotients of these three objects to be the building blocks for all <em>W</em>-algebras in classical types.</p>","abstract_has_math":false,"creators":["Kovalchuk, Vladimir"],"institution":null,"degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Andrew R. Linshaw","Florencia Orosz","Shashank Kanade","Schuyler van Engelenburg"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-06-15T07:00:00Z","date_published":"2024-06-15T07:00:00Z","updated_at":"2026-07-24T02:01:48Z","subjects":["Vertex algebras","Mathematics","Algebra","Other Mathematics","Physical Sciences and Mathematics"],"languages":["English (eng)"],"rights":["Copyright is held by the author. User is responsible for all copyright compliance.
"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.du.edu/etd/2405","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Andrew R. Linshaw","Florencia Orosz","Shashank Kanade","Schuyler van Engelenburg"]},{"key":"dc:creator","label":"Author","values":["Kovalchuk, Vladimir"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Vertex algebras","Mathematics","Algebra","Other Mathematics","Physical Sciences and Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English (eng)"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright is held by the author. User is responsible for all copyright compliance.
"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.du.edu/etd/2405"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The universal 2-parameter vertex algebra W∞ of type W(2, 3, 4; . . . ) serves as a classifying object for vertex algebras of type W(2, 3, . . . ,N) for some N in the sense that under mild hypothesis, all such vertex algebras arise as quotients of W∞. There is an ℕ X ℕ family of such 1-parameter vertex algebras known as Y-algebras. They were introduced by Gaiotto and Rapčák are expected to be building blocks for all W-algebras in type A, i.e, every W-(super) algebra in type A is an extension of a tensor product of finitely many Y-algebras. Similarly, the orthosymplectic Y-algebras are 1-parameter quotients of a universal 2-parameter vertex algebra of type W(2, 4, 6, . . . ), which is a classifying object for vertex algebras of type W(2, 4, . . . , 2N) for some N. Unlike type A, these algebras are not all the building blocks for W-algebras of types B, C, and D. In this thesis, we construct a new universal 2-parameter vertex algebra of type W(13, 2, 33, 4, 53, 6, . . . ) which we denote by W∞sp since it contains a copy of the affine vertex algebra Vk(sp2). We identify 8 infinite families of 1-parameter quotients W∞sp which are analogues of the Y-algebras, and 4 infinite families with sp2-level constant. We regard W∞sp as a fundamental object on equal footing with W∞ and W∞ev, and we give some heuristic reasons for why we expect the 1-parameter quotients of these three objects to be the building blocks for all W-algebras in classical types.
"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Building Blocks for W-Algebras of Classical Types"]}]}],"canonical_facts":{"dc:contributor":["Andrew R. Linshaw","Florencia Orosz","Shashank Kanade","Schuyler van Engelenburg"],"dc:creator":["Kovalchuk, Vladimir"],"dc:description.abstract":["The universal 2-parameter vertex algebra W∞ of type W(2, 3, 4; . . . ) serves as a classifying object for vertex algebras of type W(2, 3, . . . ,N) for some N in the sense that under mild hypothesis, all such vertex algebras arise as quotients of W∞. There is an ℕ X ℕ family of such 1-parameter vertex algebras known as Y-algebras. They were introduced by Gaiotto and Rapčák are expected to be building blocks for all W-algebras in type A, i.e, every W-(super) algebra in type A is an extension of a tensor product of finitely many Y-algebras. Similarly, the orthosymplectic Y-algebras are 1-parameter quotients of a universal 2-parameter vertex algebra of type W(2, 4, 6, . . . ), which is a classifying object for vertex algebras of type W(2, 4, . . . , 2N) for some N. Unlike type A, these algebras are not all the building blocks for W-algebras of types B, C, and D. In this thesis, we construct a new universal 2-parameter vertex algebra of type W(13, 2, 33, 4, 53, 6, . . . ) which we denote by W∞sp since it contains a copy of the affine vertex algebra Vk(sp2). We identify 8 infinite families of 1-parameter quotients W∞sp which are analogues of the Y-algebras, and 4 infinite families with sp2-level constant. We regard W∞sp as a fundamental object on equal footing with W∞ and W∞ev, and we give some heuristic reasons for why we expect the 1-parameter quotients of these three objects to be the building blocks for all W-algebras in classical types.
"],"dc:format":["application/pdf"],"dc:identifier":["https://digitalcommons.du.edu/etd/2405"],"dc:language":["English (eng)"],"dc:rights":["Copyright is held by the author. User is responsible for all copyright compliance.
"],"dc:subject":["Vertex algebras","Mathematics","Algebra","Other Mathematics","Physical Sciences and Mathematics"],"dc:title":["Building Blocks for W-Algebras of Classical Types"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-24T02:01:48Z"}