Accession Number : AD0615146

Title :   COHOMOLOGY AND DEFORMATIONS IN GRADED LIE ALGEBRAS,

Corporate Author : WASHINGTON UNIV SEATTLE

Personal Author(s) : Nijenhuis,Albert ; Richardson,R. W. ,Jr.

Report Date : MAY 1965

Pagination or Media Count : 50

Abstract : The theories of deformations of associative algebras, Lie algebras, and of representations and homomorphisms of these all show a striking similarity to the theory of deformations of complex analytic manifolds. The common context of all these turns out to be the problem of deforming one single element x of degree one in a graded Lie algebra subject to the condition (x,x) = 0. The first part of this report gives general properties of graded Lie algebras over fields of characteristic not 2; the second part deals with the case of characteristic 2. The third and fourth parts give general theorems on deformability for the respective cases when the base field is the real or complex numbers (analytic methods), and general algebraically closed fields (algebraic methods). It is shown that deformability is to a large extent determined by certain cohomology groups and mappings of these. (Author)

Descriptors :   (*ALGEBRAIC TOPOLOGY, GROUPS (MATHEMATICS)), (*ALGEBRAS, GROUPS (MATHEMATICS)), ALGEBRAIC GEOMETRY, MAPPING (TRANSFORMATIONS), THEOREMS

Distribution Statement : APPROVED FOR PUBLIC RELEASE