n. a topological group that can be given an analytic structure such that the group operation and inversion are analytic. Thus, the coordinates of the product of two elements are analytic functions of the coordinates of the elements. See manifold. (Named after the Norwegian group theorist, analyst, and geometer, Marius Sophus Lie (1842-99), who collaborated with Felix Klein and succeeded him as Professor in Leipzig. He developed the theory of invariance and made substantial contributions to the theory of differential equations.)