The W3 Algebra
Subtitle: Modules, Semi-Infinite Cohomology and Bv Algebras (Lecture Notes in Physics New Series M)
Publisher: Springer
Published: November 1996
Language: eng
Format: Hardcover
Number of pages: 204
ISBN-13: 9783540615286
Subjects: Algebra; Geophysics; Mathematics for scientists & engineers; Quantum physics (quantum mechanics); Mathematics; C*-algebras; Science; Science/Mathematics; Physics; Algebra - Linear; Homology Theory; Mathematical Physics
Description: W algebras are nonlinear generalizations of Lie algebras that arise in the context of two-dimensional conformal field theories when one explores higher-spin extensions of the Virasoro algebra. They provide the underlying symmetry algebra of certain string generalizations which allow the extended world sheet gravity. This book presents such gravity theories, concentrating on the algebra of physical operators determined from an analysis of the corresponding BRST cohomology. It develops the representation theory of W algebras needed to extend the standard techniques which were so successful in treating linear algebras. For certain strings corresponding to WN gravity we show that the operator cohomology has a natural geometric model. This result suggests new directions for the study of W geometry.