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An application of the second isomorphism theorem identifies projective linear groups: for example, the group on the complex projective line starts with setting = (), the group of invertible 2 × 2 complex matrices, = (), the subgroup of determinant 1 matrices, and the normal subgroup of scalar matrices = {():}, we have = {}, where is ...
Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law. This is the first of two theorems (see Noether's second theorem ) published by the mathematician Emmy Noether in 1918. [ 1 ]
Her work on differential invariants in the calculus of variations, Noether's theorem, has been called "one of the most important mathematical theorems ever proved in guiding the development of modern physics". [11] In the second epoch (1920–1926), she began work that "changed the face of [abstract] algebra". [12]
Envelope theorem (calculus of variations) Isoperimetric theorem (curves, calculus of variations) Minimax theorem (game theory) Mountain pass theorem (calculus of variations) Noether's second theorem (calculus of variations, physics) Parthasarathy's theorem (game theory) Sion's minimax theorem (game theory) Tonelli's theorem (functional analysis)
Emmy Noether (1882–1935), German Jewish mathematician; Herglotz–Noether theorem, in special relativity; Lasker–Noether theorem, that states that every Noetherian ring is a Lasker ring; Skolem–Noether theorem, which characterizes the automorphisms of simple rings; Albert–Brauer–Hasse–Noether theorem, in algebraic number theory
In mathematics, the Riemann–Roch theorem for surfaces describes the dimension of linear systems on an algebraic surface. The classical form of it was first given by Castelnuovo ( 1896 , 1897 ), after preliminary versions of it were found by Max Noether ( 1886 ) and Enriques ( 1894 ).
Noether's theorem (or Noether's first theorem) Noether's second theorem; Noether normalization lemma; Noetherian rings; Nöther crater, on the far side of the Moon, named after Emmy Noether; Fritz Noether (1884–1941), professor at the University of Tomsk; Gottfried E. Noether (1915–1991), son of Fritz Noether, statistician at the University ...
Being Lagrangian symmetries, gauge symmetries of a Lagrangian satisfy Noether's first theorem, but the corresponding conserved current takes a particular superpotential form = + where the first term vanishes on solutions of the Euler–Lagrange equations and the second one is a boundary term, where is called a superpotential.