Lie group

In mathematics, a Lie group is an analytic real or complex manifold that is also a group such that the group operations multiplication and inversion are analytic maps. Lie groups are important in mathematical analysis, physics and geometry because they serve to describe the symmetry of analytical structures. They were introduced by Sophus Lie in 1870 in order to study symmetries of differential equations.

References

• Wulf Rossmann, Lie Groups: An Introduction Through Linear Groups (Oxford Graduate Texts in Mathematics), Oxford University Press ISBN 0-19-859683-9. Be sure to get hold of the 2003 reprinting or later, which corrects some unfortunate typos that would otherwise slightly mar an excellent learning adventure.