Spinor Construction of Vertex Operator Algebras Triality, ans E8. Contemporary Mathematics, Vol. 121
Language: English
Published by Rhode Island, American Mathematical Society., 1991
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146 p., with numerous figures, 25 cm. Good condition. Sprache: Englisch Gewicht in Gramm: 395.
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- Title
- Spinor Construction of Vertex Operator Algebras Triality, ans E8. Contemporary Mathematics, Vol. 121
- Author
- Feingold, Alex J. et. al.:
- Publisher
- Rhode Island, American Mathematical Society.
- Publication year
- 1991
- Condition
- Gut
- Binding
- Paperback.
- Language
- English
- ISBN 10
- 0821851284
- ISBN 13
- 9780821851289
- Item weight
- 395 grams
- Seller catalogs
- Varia
operators for modules of vertex operator algebras yield braid group representations and leads to natural generalizations of vertex operator algebras, such as superalgebras and para-algebras. Many examples of vertex operator algebras and their generalizations are related to constructions in classical representation theory and shed new light on the classical theory.
This book accomplishes several goals. The authors provide an explicit spinor construction, using only Clifford algebras, of a vertex operator superalgebra structure on the direct sum of the basic and vector modules for the affine Kac-Moody algebra Dn(1). They also review and extend Chevalley's spinor construction of the 24-dimensional commutative nonassociative algebraic structure and triality on the direct sum of the three 8-dimensional D4-modules. Vertex
operator para-algebras, introduced and developed independently in this book and by Dong and Lepowsky, are related to one-dimensional representations of the braid group. The authors also provide a unified approach to the Chevalley, Greiss, and E8 algebras and explain some of their similarities. A Third goal is to provide a purely spinor construction of the exceptional affine Lie algebra E8(1), a natural continuation of previous work on spinor and oscillator
constructions of the classical affine Lie algebras. These constructions
should easily extend to include the rest of the exceptional affine Lie algebras. The final objective is to develop an inductive technique of construction which could be applied to the Monster vertex operator algebra.
Directed at mathematicians and physicists, this book should be accessible to graduate students with some background in finite-dimensional Lie algebras and their representations. Although some experience with affine Kac-Moody algebras would be useful, a summary of the relevant parts of that theory is included. This book shows how the concepts and techniques of Lie theory can be generalized to yield the algebraic structures associated with conformal field theory. The careful reader will also
gain a detailed knowledge of how the spinor construction of classical triality lifts to the affine algebras and plays an important role in the spinor construction of vertex operator algebras, modules, and intertwining operators with nontrivial monodromies.
"Synopsis" may belong to another edition of this title.
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