The Book of Dreams (Jack Vance novel) in the free inaugural issue as part of a contest, offering large cash prizes to anyone who can first identify any or all of the ten people in the photograph. An attractive red-haired young woman, Alice Wroke, seeks temporary employment processing the contest entries. Gersen, expecting an attempt at infiltration by Treesong, covertly uses a lie detector on her and confirms his suspicions. Eventually, each of the subjects is identified, except for one man who seems to have a variety of identities. When a contestant submits the correct identification for all ten, Gersen confronts Alice and places most of his
Lie group symmetries include rotation about an axis. What must be understood is the nature of 'small' transformations, for example, rotations through tiny angles, that link nearby transformations. The mathematical object capturing this structure is called a Lie algebra (Lie himself called them "infinitesimal groups"). It can be defined because Lie groups are smooth manifolds, so have tangent spaces at each point. The Lie algebra of any compact Lie group (very roughly: one for which the symmetries form a bounded set) can be decomposed as a direct sum of an abelian Lie algebra and some number of simple ones. The structure of