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Register a new userTwisted modules for quantum vertex algebras
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We study twisted modules for (weak) quantum vertex algebras and we give a conceptual construction of (weak) quantum vertex algebras and their twisted modules. As an application we construct and classify irreducible twisted modules for a certain family of quantum vertex algebras.
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This is a paper in a series systematically to study toroidal vertex algebras. Previously, a theory of toroidal vertex algebras and modules was developed and toroidal vertex algebras were explicitly associated to toroidal Lie algebras. In this paper, we study twisted modules for toroidal vertex algebras. More specifically, we introduce a notion of twisted module for a general toroidal vertex algebra with a finite order automorphism and we give a general construction of toroidal vertex algebras and twisted modules. We then use this construction to establish a natural association of toroidal vertex algebras and twisted modules to twisted toroidal Lie algebras. This together with some other known results implies that almost all extended affine Lie algebras can be associated to toroidal vertex algebras.
We study $N$-graded $phi$-coordinated modules for a general quantum vertex algebra $V$ of a certain type in terms of an associative algebra $widetilde{A}(V)$ introduced by Y.-Z. Huang. Among the main results, we establish a bijection between the set of equivalence classes of irreducible $N$-graded $phi$-coordinated $V$-modules and the set of isomorphism classes of irreducible $widetilde{A}(V)$-modules. We also show that for a vertex operator algebra, rationality, regularity, and fusion rules are independent of the choice of the conformal vector.
This paper is about $phi$-coordinated modules for weak quantum vertex algebras. Among the main results, several canonical connections among $phi$-coordinated modules for different $phi$ are established. For vertex operator algebras, a reinterpretation of Frenkel-Huang-Lepowskys theorem on contragredient module is given in terms of $phi$-coordinated modules.
We study $phi_epsilon$-coordinated modules for vertex algebras, where $phi_epsilon$ with $epsilon$ an integer parameter is a family of associates of the one-dimensional additive formal group. As the main results, we obtain a Jacobi type identity and a commutator formula for $phi_epsilon$-coordinated modules. We then use these results to study $phi_epsilon$-coordinated modules for vertex algebras associated to Novikov algebras by Primc.
We develop a theory of toroidal vertex algebras and their modules, and we give a conceptual construction of toroidal vertex algebras and their modules. As an application, we associate toroidal vertex algebras and their modules to toroidal Lie algebras.
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