A new construction of vertex algebras and quasi-modules for vertex algebras |
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Authors: | Haisheng Li |
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Institution: | a Department of Mathematical Sciences, Rutgers University, Camden, NJ 08102, USA b Department of Mathematics, Harbin Normal University, Harbin, China |
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Abstract: | In this paper, a new construction of vertex algebras from more general vertex operators is given and a notion of quasimodule for vertex algebras is introduced and studied. More specifically, a notion of quasilocal subset(space) of for any vector space W is introduced and studied, generalizing the notion of usual locality in the most possible way, and it is proved that on any maximal quasilocal subspace there exists a natural vertex algebra structure and that any quasilocal subset of generates a vertex algebra. Furthermore, it is proved that W is a quasimodule for each of the vertex algebras generated by quasilocal subsets of . A notion of Γ-vertex algebra is also introduced and studied, where Γ is a subgroup of the multiplicative group C× of nonzero complex numbers. It is proved that any maximal quasilocal subspace of is naturally a Γ-vertex algebra and that any quasilocal subset of generates a Γ-vertex algebra. It is also proved that a Γ-vertex algebra exactly amounts to a vertex algebra equipped with a Γ-module structure which satisfies a certain compatibility condition. Finally, two families of examples are given, involving twisted affine Lie algebras and certain quantum torus Lie algebras. |
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Keywords: | Compatibility Quasimodule Quasilocal subset _method=retrieve& _eid=1-s2 0-S0001870805000885& _mathId=si13 gif& _pii=S0001870805000885& _issn=00018708& _acct=C000054348& _version=1& _userid=3837164& md5=bb635ebb6601b78f54d2899ecc743d2c')" style="cursor:pointer Γ-vertex algebra" target="_blank">" alt="Click to view the MathML source" title="Click to view the MathML source">Γ-vertex algebra |
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