Abstract
dc:description.abstract<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>
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Dissertation
- Year
- 2024
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Kovalchuk, Vladimir
- Contributors dc:contributor
-
- Andrew R. Linshaw
- Florencia Orosz
- Shashank Kanade
- Schuyler van Engelenburg
Subjects
dc:subject × 5Rights
dc:rights- Statement dc:rights
-
- <p>Copyright is held by the author. User is responsible for all copyright compliance.</p>
- Language dc:language
- English (eng)
Identifiers
dc:identifier.*- Repository record dc:identifier
- https://digitalcommons.du.edu/etd/2405
- OAI identifier oai:identifier
- oai:digitalcommons.du.edu:etd-3393