The W3 Algebra

Modules, Semi-infinite Cohomology and BV Algebras

Peter Bouwknegt, Jim McCarthy, Krzysztof Pilch (Autoren)

Buch | Softcover

XI, 204 Seiten

2013
Springer Berlin (Verlag)
978-3-662-14092-5 (ISBN)

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The study of W algebras began in 1985 in the context of two-dimensional conf- mal field theories, the aim being to explore higher-spin extensions of the Virasoro algebra. Given the simultaneous growth in the understanding of two-dimensional metric gravity inspired by analyses of string models, it was inevitable that these algebras would be applied to give analogues of putative higher-spin gravity t- ories. This book is an exposition of the past few years of our work on such an application for the algebra: in particular, the BRST quantization of the n- critical 4D string. We calculate the physical spectrum as a problem in BRST cohomology. The corresponding operator cohomology forms a BV algebra, for which we provide a geometrical model. The algebra has one further generator, of spin three, in addition to the (spin two) energy-momentum tensor which generates the Virasoro algebra. C- trary to the Virasoro algebra, it is an algebra defined by nonlinear relations. In deriving our understanding of the resulting gravity theories we have had to - velop a number of results on the representation theory of W algebras, to replace the standard techniques that were so successful in treating linear algebras.

and Preliminaries.- W Algebras and Their Modules.- BRST Cohomology of the 4D W3 String.- Batalin-Vilkovisky Algebras.- The BV Algebra of the W3 String.

Erscheint lt. Verlag	13.11.2013
Reihe/Serie	Lecture Notes in Physics Monographs
Zusatzinfo	XI, 204 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	316 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Algebra • cohomology • Field • Geometry • Gravity • Lie algebra • linear algebra • Quantum Gravity • Representation Theory • Virasaro algebra • W -geometry • W*-geometry
ISBN-10	3-662-14092-6 / 3662140926
ISBN-13	978-3-662-14092-5 / 9783662140925
Zustand	Neuware