Lie detection Lie detector results are very rarely admitted in evidence in the US courts. In 1983 the U.S. Congress Office of Technology Assessment published a review of the technology and found: In the 2007 peer-reviewed academic article "Charlatanry in forensic speech science", the authors reviewed 50 years of lie detector research and came to the conclusion that there is no scientific evidence supporting that voice analysis lie detectors actually work. Lie detector manufacturer Nemesysco threatened to sue the academic publisher for libel resulting in removal of the article from online databases. In a letter to the publisher, Nemesysco's lawyers wrote that
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