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Bosonic construction of vertex operator para-algebras from symplectic affine Kac-Moody algebras.

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060526s1994 eng d

099		AAI9434055
035		\|aAAI9434055
035		\|a(UnM)AAI9434055
040		\|aUnM\|cUnM
095		\|pBOOK\|d510s\|eW431
100	1	\|aWeiner, Michael David.
245	10	\|aBosonic construction of vertex operator para-algebras from symplectic affine Kac-Moody algebras.
300		\|a120 p.
500		\|aSource: Dissertation Abstracts International, Volume: 55-08, Section: B, page: 3358.
500		\|aSupervisor: Alex J. Feingold.
502		\|aThesis (Ph.D.)--State University of New York at Binghamton, 1994.
520		\|aThe representation theory of affine Kac-Moody Lie algebras has grown tremendously since their independent introduction by Robert V. Moody and Victor G. Kac in 1968. The Virasoro algebra is another infinite dimensional Lie algebra whose theory is inextricably intertwined with the theory of affine Kac-Moody algebras. Inspired by mathematical structures found by theoretical physicists, and by the desire to understand the "monstrous moonshine" of the Monster group, the theory of vertex operator algebras (VOA's) was introduced by Borcherds, Frenkel, Lepowsky and Meurman. A representation of the Virasoro algebra is a key point in the definition of VOA's. In a very important class of examples, one also has a representation of an affine algebra, so this new theory unifies and vastly extends the representation theories of both kinds of infinite dimensional Lie algebras. An important subject in this young field is the study of modules for VOA's and intertwining operators between modules. Feingold, Frenkel and Ries defined a structure, called a vertex operator para-algebra (VOPA), where a VOA, its modules and their intertwining operators are unified. The definitions of these structures are rather complicated and the actual construction of specific examples can be a significant task. In this work, for each \|l \ge 1\|, we begin with the bosonic construction (from a Weyl algebra) of four level -\|1\over 2\| irreducible representations of the symplectic affine Kac-Moody Lie algebra \|C\sb{l}\sp{(1)}\|. The direct sum of two of these is given the structure of a VOA, and the direct sum of the other two is given the structure of a twisted VOA-module. In order to define intertwining operators so that the whole structure forms a VOPA, it is necessary to separate the four irreducible modules, taking one as the VOA and the others as modules for it. This work includes the bosonic analog of the fermionic construction of a vertex operator superalgebra from the four level 1 irreducible modules of type given by Feingold, Frenkel and Ries. While they only get a VOPA when l = 4 using classical triality, the techniques in this work apply to any \|l \ge 1
590		\|aSchool code: 0792.
650	4	\|aMathematics.
690		\|a0405
710	20	\|aState University of New York at Binghamton.
773	0	\|tDissertation Abstracts International\|g55-08B.
790		\|a0792
790	10	\|aFeingold, Alex J.,\|eadvisor
791		\|aPh.D.
792		\|a1994
856	40	\|uhttp://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9434055

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Bosonic construction of vertex operator para-algebras from symplectic affine Kac-Moody algebras.

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