ϕ-Coordinated modules for quantum vertex algebras and associative algebras

We study N-graded ϕ-coordinated modules for a general quantum vertex algebra V of a certain type in terms of an associative algebra A˜(V) introduced by Y.-Z. Huang. Among the main results, we associate a sequence of associative algebras A˜n(V) for n∈N with A˜0(V)=A˜(V) and we establish a bijection b...

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Bibliographic Details
Published in:Journal of algebra 2018-03, Vol.498, p.1-37
Main Author: Li, Haisheng
Format: Article
Language:English
Subjects:
Quantum vertex algebra
Vertex super-algebra
Zhu algebra
ϕ-Coordinated module
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Summary:We study N-graded ϕ-coordinated modules for a general quantum vertex algebra V of a certain type in terms of an associative algebra A˜(V) introduced by Y.-Z. Huang. Among the main results, we associate a sequence of associative algebras A˜n(V) for n∈N with A˜0(V)=A˜(V) and we establish a bijection between the set of equivalence classes of irreducible N-graded ϕ-coordinated V-modules and the set of isomorphism classes of irreducible 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.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2017.11.022