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Introduction to Vertex Operator Superalgebras and Their Modules (Paperback, Softcover reprint of hardcover 1st ed. 1998)
Loot Price: R4,527
Discovery Miles 45 270
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Introduction to Vertex Operator Superalgebras and Their Modules (Paperback, Softcover reprint of hardcover 1st ed. 1998)
Series: Mathematics and Its Applications, 456
Expected to ship within 10 - 15 working days
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Vertex algebra was introduced by Boreherds, and the slightly
revised notion "vertex oper- ator algebra" was formulated by
Frenkel, Lepowsky and Meurman, in order to solve the problem of the
moonshine representation of the Monster group - the largest
sporadie group. On the one hand, vertex operator algebras ean be
viewed as extensions of eertain infinite-dimensional Lie algebras
such as affine Lie algebras and the Virasoro algebra. On the other
hand, they are natural one-variable generalizations of commutative
associative algebras with an identity element. In a certain sense,
Lie algebras and commutative asso- ciative algebras are reconciled
in vertex operator algebras. Moreover, some other algebraie
structures, such as integral linear lattiees, Jordan algebras and
noncommutative associa- tive algebras, also appear as subalgebraic
structures of vertex operator algebras. The axioms of vertex
operator algebra have geometrie interpretations in terms of Riemman
spheres with punctures. The trace functions of a certain component
of vertex operators enjoy the modular invariant properties. Vertex
operator algebras appeared in physies as the fundamental algebraic
structures of eonformal field theory, whieh plays an important role
in string theory and statistieal meehanies.
Moreover,eonformalfieldtheoryreveals
animportantmathematiealproperty,the so called "mirror symmetry"
among Calabi-Yau manifolds. The general correspondence between
vertex operator algebras and Calabi-Yau manifolds still remains
mysterious. Ever since the first book on vertex operator algebras
by Frenkel, Lepowsky and Meur- man was published in 1988, there has
been a rapid development in vertex operator su- peralgebras, which
are slight generalizations of vertex operator algebras.
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