| 释义 |
Lie, n.3|liː|
The name of Sophus Lie (1842–99), Norwegian mathematician, used attrib. to denote certain concepts investigated by him, as Lie algebra, a vector space extending over a field in which a product operation (×) is defined such that for all x, y, z in the space x × y is bilinear, x × x = 0, and (x × y) × z + (y × z) × x + (z × x) × y = 0; Lie group, a topological group in which it is possible to label the group elements by a finite number of coordinates in such a way that the coordinates of the product of two elements are analytic functions of the coordinates of the two elements and the coordinates of the inverse of an element are analytic functions of the coordinates of that element.
1935Bull. Amer. Math. Soc. XLI. 344 A Lie algebra L over a non-modular field F will be called normal simple over F if H is an algebraically closed extension of F and LH is a simple algebra. 1939H. Weyl Classical Groups vii. 188 The process of averaging over a compact Lie group presupposes our ability to compare volume elements at different points of the group manifold. 1965H. J. Lipkin Lie Groups for Pedestrians i. 14 The use of the Lie algebra therefore simplifies the solution of the eigenvalue problem for the Hamiltonian by defining a number of integrals of the motion. 1967G. Steiner Lang. & Silence 33 One cannot ‘translate’ the conventions and notations governing the operations of Lie groups..into any words or grammar outside mathematics. 1969Sci. News 31 May 538 The mathematical name of these patterns is Lie groups or unitary symmetry groups. They have been used to predict the existence of new [subatomic] particles. |