A Lie algebra is a nonassociative algebra corresponding to a Lie group.

A nonassociative algebra obeyed by objects such as the Lie bracket and Poisson bracket. Elements f, g, and h of a Lie algebra satisfy [f, f] = 0 [f + g, h] = [f, h] + [g, h], and [f, [g, h]] + [g, [h, f]] + [h, [f, g]] = 0 (the Jacobi identity). The relation [f, f] = 0 implies [f, g] = - [g, f]. For characteristic not equal to two, these two relations are equivalent. The binary operation of a Lie algebra is the bracket [f g, h] = f[g, h] + [f, h] g.

Ado's theorem | derivation algebra | Dynkin diagram | Iwasawa's theorem | Jacobi identities | Lie algebroid | Lie bracket | Lie group | Poincaré-Birkhoff-Witt theorem | Poisson bracket | reduced root system | root system | Weyl group

graduate school level

Marius Sophus Lie