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Integral forms for certain classes of vertex operator algebras and their modules

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Title
Integral forms for certain classes of vertex operator algebras and their modules
Name (type = personal)
NamePart (type = family)
McRae
NamePart (type = given)
Robert H.
NamePart (type = date)
1987-
DisplayForm
Robert McRae
Role
RoleTerm (authority = RULIB)
author
Name (type = personal)
NamePart (type = family)
Lepowsky
NamePart (type = given)
James
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James Lepowsky
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Advisory Committee
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chair
Name (type = personal)
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HUANG
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YI-ZHI
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YI-ZHI HUANG
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Advisory Committee
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internal member
Name (type = personal)
NamePart (type = family)
Li
NamePart (type = given)
Haisheng
DisplayForm
Haisheng Li
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Milas
NamePart (type = given)
Antun
DisplayForm
Antun Milas
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
outside member
Name (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (type = corporate)
NamePart
Graduate School - New Brunswick
Role
RoleTerm (authority = RULIB)
school
TypeOfResource
Text
Genre (authority = marcgt)
theses
OriginInfo
DateCreated (qualifier = exact)
2014
DateOther (qualifier = exact); (type = degree)
2014-05
Place
PlaceTerm (type = code)
xx
Language
LanguageTerm (authority = ISO639-2b); (type = code)
eng
Abstract (type = abstract)
We study integral forms in vertex operator algebras over $mathbb{C}$. We prove general results on when a multiple of the standard conformal vector $omega$ can be added to an integral form of a vertex operator algebra and when intertwining operators among modules for a vertex operator algebra respect integral forms in the modules. We also show when the $mathbb{Z}$-dual of an integral form in a module for a vertex operator algebra is an integral form in the contragredient module. As examples, we consider vertex operator algebras based on affine Lie algebras and even lattices, and tensor powers of the Virasoro vertex operator algebra $L(frac{1}{2},0)$. In particular, we demonstrate vertex algebraic generators of integral forms for standard modules for affine Lie algebras that were first constructed in work of Garland; we reprove Borcherds' construction of integral forms in lattice conformal vertex algebras using generators; and we find generating sets that include $omega$ for integral forms in tensor powers $L(frac{1}{2},0)^{otimes n}$ when $nin 4mathbb{Z}$. We also construct integral forms in modules for these vertex operator algebras using generating sets, and we show when intertwining operators among modules for these vertex operator algebras respect integral forms in the modules.
Subject (authority = RUETD)
Topic
Mathematics
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_5425
PhysicalDescription
Form (authority = gmd)
electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
vi, 95 p. : ill.
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Robert H. McRae
Subject (authority = ETD-LCSH)
Topic
Vertex operator algebras
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier (type = doi)
doi:10.7282/T3KS6PV2
Genre (authority = ExL-Esploro)
ETD doctoral
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The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
McRae
GivenName
Robert
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2014-04-09 22:50:03
AssociatedEntity
Name
Robert McRae
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
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Author Agreement License
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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Copyright protected
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RULTechMD (ID = TECHNICAL1)
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ETD
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windows xp
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