∞-Lie theory

# Contents

## Definition

A Lie algebra $\mathfrak{g}$ is called reductive if the following equivalence conditions hold:

1. it is the direct sum $\mathfrak{g} \simeq \mathfrak{h} \oplus \mathfrak{a}$ of a semisimple Lie algebra $\mathfrak{h}$ and an abelian Lie algebra $\mathfrak{a}$;

2. its adjoint representation is completely reducible?: every invariant subspace has an invariant complement.

## References

For instance volume III of

Revised on June 30, 2011 18:48:15 by Urs Schreiber (131.211.239.52)