Monographs in Contemporary Mathematics

Fuks, D.B.

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.

Details

Published by: Springer

Publication Date: 2012-06-12

Format: Paperback

ISBN-13: 9781468487671

DOI: 10.1007/978-1-4684-8765-7

Dimensions: 229cm x152cm

Pages: 339