Cohomology of infinite-dimensional Lie algebras
著者
書誌事項
Cohomology of infinite-dimensional Lie algebras
（Contemporary Soviet mathematics）
Consultants Bureau, c1986
- タイトル別名
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Когомологии бесконечномерных алгебр Ли
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注記
Translation of: Когомологии бесконечномерных алгебр Ли
Bibliography: p. 319-327
Includes index
内容説明・目次
内容説明
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.
目次
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.
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