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  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 . With g=1 we recover An(V) as in .
|Commitee:||Mason, Geoffrey, Boltje, Robert|
|School:||University of California, Santa Cruz|
|School Location:||United States -- California|
|Source:||DAI-B 81/7(E), Dissertation Abstracts International|
|Subjects:||Mathematics, Applied Mathematics|
|Keywords:||Orbifold theory, Representation theory, Twisted modules, Vertex operator algebra, Vertex operator superalgebra|
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