Suites inertes dans les algèbres de Lie graduées. (“Autopsie d’un meurtre. II”). (French) Zbl 0655.55004

Halperin, S.; Lemaire, J.-M.

Math. Scand. 61, No. 1, 39-67 (1987).

The paper under review rounds off a program started with the second author’s thesis about fifteen years ago, related to the module of D by N. It is then shown if M is a divisible R-module, N is a submodule of M, and \(X_ M\) is a fuzzy divisible R-module, then the map \(X:\quad M/N\to [0,1]\) given by \(X(m+N)=X'(1\otimes m+N')\) determines a fuzzy R-module where \(M'=[1\otimes m| \quad m\in M\}\subseteq S^{-1}R\otimes M\) for \(S=R-\{0\}\) and \(X':\quad M'\to [0,1]\) is given by \(X'(1\otimes m)=X(m+tor(M))\).

Reviewer: J.-N.Mordeson

MSC:

55P62	Rational homotopy theory
17B70	Graded Lie (super)algebras
55P15	Classification of homotopy type
17B55	Homological methods in Lie (super)algebras

Keywords:

Lie elements in universal enveloping algebra