Given a vector space $V$, the abelian Lie algebra on $V$, hence the Lie algebra with vanishing Lie bracket, may be thought of as the Lie algebra of $V$ regarded as an additive abelian Lie group. As such it is the translation Lie algebra of $V$.

translation group

PoincarĂ© Lie algebra

super translation Lie algebra

Last revised on August 31, 2013 at 04:12:32. See the history of this page for a list of all contributions to it.