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Representation theory and cohomology theory of meromorphic open-string vertex algebras
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Qi, Fei. Representation theory and cohomology theory of meromorphic open-string vertex algebras. Retrieved from https://doi.org/doi:10.7282/T32V2KJ9

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TitleRepresentation theory and cohomology theory of meromorphic open-string vertex algebras
NameQi, Fei (author); HUANG, YI-ZHI (chair); Lepowsky, James (internal member); Carbone, Lisa (internal member); Yang, Jinwei (outside member); Rutgers University; School of Graduate Studies
Date Created2018
Other Date2018-05 (degree)
SubjectMathematics, Vertex operator algebras
Extent1 online resource (ix, 240 p.)
DescriptionIn this dissertation we systematically study the meromorphic open-string vertex algebra, its representation theory, and its the cohomology theory. Meromorphic open-string vertex algebra (MOSVA hereafter) is a natural noncommutative generalization of vertex algebra. It is the algebraic structure of vertex operators satisfying associativity, but not necessarily commutativity. We review the axiomatic system of MOSVA and its left modules given by Huang and give the definition of right modules and bimodules. We prove that the rationality of iterates follows from the axioms. We introduce a pole-order condition which is used to simplify the axiomatic system and give a formulation by series with formal variables. We introduce the skew-symmetry operator, define the opposite MOSVA analogous to the opposite algebra of an associative algebra, and study the relation between modules for a MOSVA and modules for the opposite MOSVA. We consider the M"obius structure on MOSVA and its modules, and prove that the contragedient of a module with M"obius structure is also a module. We compute an example of MOSVA that is constructed from the two-dimensional sphere. We use rational function taking values in the algebraic completion to develop cohomology theory of MOSVA and its bimodules. We prove that the first cohomology of a MOSVA is isomorphic to the set of outer derivations. We prove also that if a MOSVA has vanishing first cohomology for every bimodule, then the its left modules of finite length and satisfying a composability condition is completely reducible.
NotePh.D.
NoteIncludes bibliographical references
Noteby Fei Qi
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/T32V2KJ9
Languageeng
CollectionSchool of Graduate Studies Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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