Cohomology of Infinite-Dimensional Lie Algebras [Paperback]

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.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 mail£‚