Spinor Construction Of Vertex Operator Algebras Triality And $E^{(1)}_8$ (CONTEMPORARY MATHEMATICS, VOL 121)

$Spinor Construction Of Vertex Operator Algebras Triality And $E^{(1)}_8$ (CONTEMPORARY MATHEMATICS, VOL 121) Mathematics$

Spinor Construction Of Vertex Operator Algebras Triality And $E^{(1)}_8$ (CONTEMPORARY MATHEMATICS, VOL 121)

Name: Spinor Construction Of Vertex Operator Algebras Triality And $E^{(1)}_8$ (CONTEMPORARY MATHEMATICS, VOL 121)
Brand: Oxford University Press
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By Frenkel, Igor B.

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Description

The theory of vertex operator algebras is a remarkably rich new mathematical field which captures the algebraic content of conformal field theory in physics. Ideas leading up to this theory appeared in physics as part of statistical mechanics and string theory. In mathematics, the axiomatic definitions crystallized in the work of Borcherds and in Vertex Operator Algebras and the Monster, by Frenkel, Lepowsky, and Meurman. The structure of monodromies of intertwining 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.

Product details

Binding:: Paperback
Number of Pages:: 156
Release Date:: 1991-11-01
Publication Date:: 1991-11-01
Publisher:: Oxford University Press
Languages:: Published: English, Original: English
ISBN10:: 0821851284
Weight:: 295 g

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