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
Martin Heisenberg Martin Heisenberg Martin Heisenberg (born 7 August 1940) is a German neurobiologist and geneticist. Before his retirement in 2008, he held the professorial chair for genetics and neurobiology at the Bio Centre of the University of Würzburg. Since then, he continues his research with a senior professorship at the Rudolf Virchow Center of the University of Würzburg. Heisenberg studied chemistry and molecular biology in Munich, Tübingen and Pasadena. In 1975 he became Professor of genetics and neurobiology at the University of Würzburg. Heisenberg's work has focused on the neurogenetics of Drosophila (the fruit fly), with the aim of investigating the