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theses

In 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.

ETD_8875

Ph.D.

Includes bibliographical references

by Fei Qi

doi:10.7282/T32V2KJ9

ETD doctoral

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