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Catalogue Information
Field name	Details
Dewey Class	512.55
Dewey Class	512.482
Title	Cohomology of Infinite-Dimensional Lie Algebras ([EBook]) / by D. B. Fuks.
Author	Fuks, Dmitrij Borisovič , 1939-
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : Springer , 1986.
Physical Details	XII, 352 p. : online resource.
Series	Contemporary Soviet mathematics
ISBN	9781468487657
Summary Note	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.:
Contents note	1. 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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4684-8765-7
Links to Related Works	Subject References: Lie groups . Mathematics . Topological groups . Topological groups, Lie groups . Authors: Fuks, Dmitrij Borisovič 1939- . See Also: Fuks, D.B. . Fuks, Dmitrij Borisovič . Фукс, Дмитрий Борисович . Corporate Authors: SpringerLink (Online service) . Series: Contemporary Soviet mathematics . Classification: 512.482 . 512.55 .

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Cohomology of Infinite-Dimensional Lie Algebras

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