(Halvdan) (1896-1968) Norwegian Labour politician and diplomat. He became secretary of the Labour Party in 1926. During the German occupation of Norway in World War II he was foreign minister in the exiled government 1941–46, when he helped retain the Norwegian fleet for the Allies. He became the first secretary-general of the United Nations 1946–53, but resigned over Soviet opposition to his handling of the Korean War.
(1842-1899) Norwegian mathematician who provided the foundations for the science of topology in transformation groups known as the Lie groups. He was one of the first mathematicians to emphasize the importance of the notion of groups in geometry.
Lie was born near Bergen and studied at Christiania (now Oslo) and abroad at Berlin and Paris. He was professor at Christiania 1873–86 and 1898–99 and at Leipzig, Germany, 1886–98.
Lie's first great discovery, made in 1870, was that of his contact transformation, which mapped straight lines with spheres and principal tangent curves into curvature lines. In his theory of tangential transformations occurs the particular transformation that makes a sphere correspond to a straight line. By 1873 Lie had begun to investigate transformation groups. In this work on group theory he chose a new space element, the contact element, which is an incidence pair of point and line or of point and hyperplane. This led him to the discovery of Lie groups, one of the basic notions of which is that of infinitesimal transformation.
The Lie integration theorem, which he developed, made it possible to classify partial differential equations in such a way as to make most of the classical methods of solving such equations reducible to a single principle.
ETYM as. lyge; akin to Dutch leugen, Old High Germ. lugi, German lüge, lug, Icel. lygi, Dan. and Swed. lögn, Goth. liugn. Related to Lie to utter a falsehood.
1. A statement that deviates from or perverts the truth; SYN. prevarication.
2. Position or manner in which something is situated.
(Irregular preterit, past participle: lay, lain).
1. To assume a resting position, as on a flat surface.
2. To be and remain in a particular state or condition.
3. To be located or situated somewhere; occupy a certain position.
4. To be lying, be prostrate; be in a horizontal position;l.
5. To have a place in relation to something else; SYN. rest.
(Irregular preterit, past participle: lied).
1. To tell an untruth; pretend with intent to deceive.
2. To make an untrue statement with intent to deceive.
3. To create a false or misleading impression.
4. To bring about by telling lies.