Date of Award

6-15-2024

Document Type

Dissertation

Degree Name

Ph.D.

Organizational Unit

College of Natural Science and Mathematics, Mathematics

First Advisor

Andrew R. Linshaw

Second Advisor

Florencia Orosz

Third Advisor

Shashank Kanade

Fourth Advisor

Schuyler van Engelenburg

Keywords

Vertex algebras, Mathematics

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.

Copyright Date

6-2024

Copyright Statement / License for Reuse

All Rights Reserved
All Rights Reserved.

Publication Statement

Copyright is held by the author. User is responsible for all copyright compliance.

Rights Holder

Vladimir Kovalchuk

Provenance

Received from ProQuest

File Format

application/pdf

Language

English (eng)

Extent

135 pgs

File Size

545 KB

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