2013/10/14 by Katrina Barron, Barron, Katrina, Nathan Vander Werf +1
Mathematics · Physics and Astronomy · #17B68 #17B69 #17B81 #81R10 #81T40 #81T60 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #hep-th #math.QA #msc:17B68 #msc:17B69 #msc:17B81 #msc:81R10 #msc:81T40 #msc:81T60
paper · pdf · doi:10.48550/arxiv.1310.3812
arXiv admin note: text overlap with arXiv:math/9803118, arXiv:1310.1956. Constant term in Corollary 6.5 corrected; other minor typos corrected; reference to arXiv:1401.4635 added; minor clarifications in exposition made. To appear in the International Journal of Mathematics
openalex publication_date 2013/10/14 · arxiv created 2014/01/25 · arxiv updated 2014/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 is 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.