T (g) is a representation of Gin L. This representation is the direct sum of the representations Tl, T2, ... , Tm, denoted by T = Tl EEl T2 EEl ...
Now, an infinitesimal displacement of the point x is a differential displacement that can be obtained in two ways: as the result of two successive transformations, x = f(xO; a) followed by x + dx = f(x; 8a), or directly from x + dx = f(xO; a + da);. 8) the considered parameters are connected by a relation of the form a + da =
Applications of the Theory of Groups in Mechanics and Physics by Petre P. Teodorescu, Nicolae-A.P. Nicorovici