Cohomology of Infinite-Dimensional Lie Algebras

1. Front Matter

   Pages i-xii

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2. General Theory

   • D. B. Fuks

   Pages 1-60

3. Computations

   • D. B. Fuks

   Pages 61-207

4. Applications

   • D. B. Fuks

   Pages 209-317

5. Back Matter

   Pages 319-339

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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.

• Characteristic class
• Finite
• algebra
• bordism
• boundary element method
• character
• classification
• cohomology
• form
• graph
• homology
• lie algebra
• mathematics
• real number
• theorem

• Moscow State University, Moscow, USSR

  D. B. Fuks

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