Read online or download a free book: Cohomology Of Infinite-Dimensional Lie Algebras: Contemporary Soviet Mathematics (Monographs In Contemporary Mathematics)
Publisher: Springer: 1986 edition (31 Dec. 1986)
By: D.B. Fuks (Author)
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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.
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