Generators, spanning sets and existence of twisted modules for a grading-restricted vertex (super)algebra

• Yi-Zhi Huang ^[1]
  1. [1] Rutgers University

     Rutgers University

     City of New Brunswick, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 4, 2020
• Idioma: inglés
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• Resumen

  • For a grading-restricted vertex superalgebra V and an automorphism g of V, we give a linearly independent set of generators of the universal lower-bounded generalized g-twisted V-module Mˆ[g]B constructed by the author in Huang (Commun Math Phys 377:909–945 (2020)). We prove that there exist irreducible lower-bounded generalized g-twisted V-modules by showing that there exists a maximal proper submodule of Mˆ[g]B for a one-dimensional space M. We then give several spanning sets of Mˆ[g]B and discuss the relations among elements of the spanning sets. Assuming that V is a Möbius vertex superalgebra (to make sure that lowest weights make sense) and that P(V) (the set of all numbers of the form R(α)∈[0,1) for α∈C such that e2πiα is an eigenvalue of g) has no accumulation point in R (to make sure that irreducible lower-bounded generalized g-twisted V-modules have lowest weights). Under suitable additional conditions, which hold when the twisted zero-mode algebra or the twisted Zhu’s algebra is finite dimensional, we prove that there exists an irreducible grading-restricted generalized g-twisted V-module, which is in fact an irreducible ordinary g-twisted V-module when g is of finite order. We also prove that every lower-bounded generalized module with an action of g for the fixed-point subalgebra Vg of V under g can be extended to a lower-bounded generalized g-twisted V-module.