Dissertation/Thesis Abstract

Twisted Modules for Vertex Operator Superalgebras and Associative Algebras
by Petersen, Charles, Ph.D., University of California, Santa Cruz, 2019, 78; 27665088
Abstract (Summary)

Let V be a vertex operator superalgebra and σ the order 2 automorphism associated with the superstructure of V. For a finite order automorphism g with σ(gσ)=T', we follow [8] to construct a sequence of associative algebras Ag,n(V) for n ∈ (1/T')Z+ such that Ag,n-(1/T')(V) is a quotient of Ag,n(V) . There is a bijection between the irreducible Ag,n(V) -modules which cannot factor through Ag,n-(1/T')(V) and the irreducible admissible g-twisted V-modules. These results are then applied to g-rational vertex operator superalgebras. In this case it is shown that V is g-rational if and only if all the Ag,n(V) are finite-dimensional. Taking n=0 we obtain the associative algebra Ag,n(V) constructed in [15]. With g=1 we recover An(V) as in [18].

Indexing (document details)
Advisor: Dong, Chongying
Commitee: Mason, Geoffrey, Boltje, Robert
School: University of California, Santa Cruz
Department: Mathematics
School Location: United States -- California
Source: DAI-B 81/7(E), Dissertation Abstracts International
Source Type: DISSERTATION
Subjects: Mathematics, Applied Mathematics
Keywords: Orbifold theory, Representation theory, Twisted modules, Vertex operator algebra, Vertex operator superalgebra
Publication Number: 27665088
ISBN: 9781392553565
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