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＜電子ブック＞
Cohomology of Infinite-Dimensional Lie Algebras / by D.B. Fuks
(Monographs in Contemporary Mathematics, Formerly Contemporary Soviet Mathematics)

版	1st ed. 1986.
出版者	(New York, NY : Springer US : Imprint: Springer)
出版年	1986
本文言語	英語
大きさ	XII, 352 p : online resource
著者標目	*Fuks, D.B author SpringerLink (Online service)
件　名	LCSH:Topological groups LCSH:Lie groups FREE:Topological Groups and Lie Groups
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-1-4684-8765-7

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