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Titlebook: Generalized Vertex Algebras and Relative Vertex Operators; Chongying Dong,James Lepowsky Book 1993 Springer Science+Business Media New Yor

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书目名称Generalized Vertex Algebras and Relative Vertex Operators
编辑Chongying Dong,James Lepowsky
视频video
丛书名称Progress in Mathematics
图书封面Titlebook: Generalized Vertex Algebras and Relative Vertex Operators;  Chongying Dong,James Lepowsky Book 1993 Springer Science+Business Media New Yor
描述In the past few years, vertex operator algebra theory has been growing both in intrinsic interest and in the scope of its interconnections with areas of mathematics and physics. The structure and representation theory of vertex operator algebras is deeply related to such subjects as monstrous moonshine, conformal field theory and braid group theory. Vertex operator algebras are the mathematical counterpart of chiral algebras in conformal field theory. In the Introduction which follows, we sketch some of the main themes in the historical development and mathematical and physical motivations of these ideas, and some of the current issues. Given a vertex operator algebra, it is important to consider not only its modules (representations) but also intertwining operators among the mod­ ules. Matrix coefficients of compositions of these operators, corresponding to certain kinds of correlation functions in conformal field theory, lead natu­ rally to braid group representations. In the specialbut important case when these braid group representations are one-dimensional, one can combine the modules and intertwining operators with the algebra to form a structure satisfying axioms fairly clos
出版日期Book 1993
关键词Algebraic structure; Cohomology; Lattice; Representation theory; algebra; cls; homology; ring theory
版次1
doihttps://doi.org/10.1007/978-1-4612-0353-7
isbn_softcover978-1-4612-6721-8
isbn_ebook978-1-4612-0353-7Series ISSN 0743-1643 Series E-ISSN 2296-505X
issn_series 0743-1643
copyrightSpringer Science+Business Media New York 1993
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Duality for generalized vertex operator algebras, rationality, generalized commutativity and generalized associativity — and we shall show that they may be used in place of the generalized Jacobi identity in the definition of generalized vertex operator algebra. These properties are aspects of “duality,” in the terminology of conformal field theor
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Tensor products,ture in fact satisfies the axioms for a generalized vertex algebra. Given a module for each of the algebras, we analogously define the notion of the tensor product module for the tensor product algebra, and we show that it is in fact a module by using the same duality argument. The definitions and r
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