COHOMOLOGY AND DEFORMATIONS IN GRADED LIE ALGEBRAS,

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)

Document Details

Document Type
Technical Report
Publication Date
May 01, 1965
Accession Number
AD0615146

Entities

People

  • Albert Nijenhuis
  • R. W. Richardson Jr.

Organizations

  • University of Washington

Tags

DTIC Thesaurus Topics

  • Complex Numbers
  • Cooperation
  • Mathematics
  • Numbers
  • Pennsylvania

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.