Heisenberg group by 90°. The other reflections are "xyx" and "yxy", and rotation by 180° is "xyxy" (="yxyx"). The Lie algebra formula_16 of the Heisenberg group formula_1 (over the real numbers) is the space of formula_18 matrices of the form with formula_20. The following three elements form a basis for formula_16: The basis elements satisfy the commutation relations: The name "Heisenberg group" is motivated by the preceding relations, which have the same form as the canonical commutation relations in quantum mechanics: where formula_25 is the position operator, formula_26 is the momentum operator, and formula_27 is Planck's constant. The Heisenberg group formula_1 has
Werner Heisenberg was placed under HWA authority, with Diebner as the administrative director, and the military control of the nuclear research commenced. During the period Diebner administered the KWIP under the HWA program, considerable personal and professional animosity developed between Diebner and Heisenberg's inner circle, which included Karl Wirtz, and Carl Friedrich von Weizsäcker. At a scientific conference on 26-28 February 1942 at the Kaiser Wilhelm Institute for Physics, called by the Army Weapons Office, Heisenberg presented a lecture to Reichs officials on energy acquisition from nuclear fission. The lecture, entitled "Die theoretischen Grundlagen für die Energiegewinning aus der Uranspaltung" was, as