HOMOGENEOUS SPACES OF INFINITE-DIMENSIONAL LIE ALGEBRAS AND CHARACTERISTIC CLASSES OF FOLIATIONS

Autor:	B I Rozenfel'd, I N Bernshtein
Rok vydání:	1973
Předmět:	Algebra Adjoint representation of a Lie algebra Representation of a Lie group General Mathematics Simple Lie group Lie group Lie theory Affine Lie algebra Representation theory Lie conformal algebra Mathematics
Zdroj:	Russian Mathematical Surveys. 28:107-142
ISSN:	1468-4829 0036-0279
DOI:	10.1070/rm1973v028n04abeh001597
Popis:	In this article we introduce a new language to describe many problems of differential geometry: for example, problems connected with the theory of pseudogroups, Lie equations, foliations, characteristic classes, etc. This is the language of infinite-dimensional Lie algebras and their homogeneous spaces. It is closely connected with the general idea of formal differential geometry set forth by I. M. Gel'fand in his lecture at the International Congress of Mathematicians in Nice. In addition to a detailed account of the theory of homogeneous spaces of infinite-dimensional Lie algebras, this article contains applications of this theory to the characteristic classes of foliations. It also includes results on these questions from earlier papers by I. M. Gel'fand, D. A. Kazhdan, D. B. Fuks, and the authors.
Databáze:	OpenAIRE
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