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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 A_{g,n}(V) for n ∈ (1/T')Z_{+} such that A_{g,n-(1/T')}(V) is a quotient of A_{g,n}(V) . There is a bijection between the irreducible A_{g,n}(V) -modules which cannot factor through A_{g,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 A_{g,n}(V) are finite-dimensional. Taking n=0 we obtain the associative algebra A_{g,n}(V) constructed in [15]. With g=1 we recover An(V) as in [18].
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 |