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- Title
PERMUTATION-TWISTED MODULES FOR EVEN ORDER CYCLES ACTING ON TENSOR PRODUCT VERTEX OPERATOR SUPERALGEBRAS.
- Authors
BARRON, KATRINA; VANDER WERF, NATHAN
- Abstract
We construct and classify (1 2 ⋯ k)-twisted V⊗k-modules for k even and V a vertex operator superalgebra. In particular, we show that the category of weak (1 2 ⋯ k)-twisted V⊗k-modules for k even is isomorphic to the category of weak parity-twisted V-modules. This result shows that in the case of a cyclic permutation of even order, the construction and classification of permutation-twisted modules for tensor product vertex operator superalgebras are fundamentally different than in the case of a cyclic permutation of odd order, as previously constructed and classified by the first author. In particular, in the even order case it is the parity-twisted V-modules that play the significant role in place of the untwisted V-modules that play the significant role in the odd order case.
- Subjects
PERMUTATION groups; MODULES (Algebra); VERTEX operator algebras; SUPERALGEBRAS; ISOMORPHISM (Mathematics); CYCLIC permutations
- Publication
International Journal of Mathematics, 2014, Vol 25, Issue 2, p-1
- ISSN
0129-167X
- Publication type
Article
- DOI
10.1142/S0129167X14500189