Cohomology of Infinite-Dimensional Lie Algebras

By D.B. Fuks

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.

• Format: Paperback
• Language: English
• ISBN: 1468487671
• ISBN13: 9781468487671
• Release Date: June 2012
• Publisher: Springer
• Length: 339 Pages
• Weight: 1.04 lbs.
• Dimensions: 0.7" x 6.0" x 9.0"