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Overview"There is no question that the cohomology of infinite dimensional Lie algebras deserves a brief and separate mono graph. This subject is not cover~d by any of the tradition al branches of mathematics and is characterized by relative ly elementary proofs and varied application. Moreover, the subject matter is widely scattered in various research papers or exists only in verbal form. The theory of infinite-dimensional Lie algebras differs markedly from the theory of finite-dimensional Lie algebras in that the latter possesses powerful classification theo rems, which usually allow one to ""recognize"" any finite dimensional Lie algebra (over the field of complex or real numbers), i.e., find it in some list. There are classifica tion theorems in the theory of infinite-dimensional Lie al gebras as well, but they are encumbered by strong restric tions of a technical character. These theorems are useful mainly because they yield a considerable supply of interest ing examples. We begin with a list of such examples, and further direct our main efforts to their study." Full Product DetailsAuthor: D.B. FuksPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: Softcover reprint of the original 1st ed. 1986 Dimensions: Width: 15.20cm , Height: 1.90cm , Length: 22.90cm Weight: 0.516kg ISBN: 9781468487671ISBN 10: 1468487671 Pages: 339 Publication Date: 12 June 2012 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of Contents1. General Theory.- §1. Lie algebras.- §2. Modules.- §3. Cohomology and homology.- §4. Principal algebraic interpretations of cohomology.- §5. Main computational methods.- §6. Lie superalgebras.- 2. Computations.- §1. Computations for finite-dimensional Lie algebras.- §2. Computations for Lie algebras of formal vector fields. General results.- §3. Computations for Lie algebras of formal vector fields on the line.- §4. Computations for Lie algebras of smooth vector fields.- §5. Computations for current algebras.- §6. Computations for Lie superalgebras.- 3. Applications.- §1. Characteristic classes of foliations.- §2. Combinatorial identities.- §3. Invariant differential operators.- §4. Cohomology of Lie algebras and cohomology of Lie groups.- §5. Cohomology operations in cobordism theory..- References.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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