Sophus Lie

Marius Sophus Lie [li ː ] ( born December 17, 1842 in Nordfjordeid, † February 18, 1899 in Kristiania, now Oslo ) was a Norwegian mathematician.

Life

Lie studied from 1859 to 1865 in Christiania (later Kristiania, now Oslo ) Natural Sciences and heard in 1862 when Peter Ludwig Sylow Mejdell lectures on group theory. He put 1865, the school teacher exam from and was initially undecided about his future career. It was not until 1868, he turned to mathematics. His first mathematical publication, which appeared in 1869, a travel grant, brought him. This he used among other things to stay in Berlin, Göttingen and Paris. Crucial to Read more career was the acquaintance and friendship with Felix Klein, with whom he traveled in 1870 to Paris and wrote joint work on transformation groups. In 1872 Professor Lie in Christiania, and in 1886 he was appointed as successor to Klein ( who moved to Göttingen ) to Leipzig appointed. Lie suffered - as later was diagnosed - with pernicious anemia, which led, together with difficulties in the scientific environment in 1889 to a nervous breakdown. In addition, Lie quarreled with his staff Friedrich Engel and Klein priority issues. From 1892 Norwegian personalities, especially Nansen, Bjornson and Elling Holst tried to return Lies, on the one hand out of concern for him, on the other, national-patriotic reasons. 1894 gave him the Norwegian Parliament a personal professorship with a corresponding salary increase in Christiania. Lie returned but only seriously ill in 1898 to Norway and taught privately or one of his most nachgefolgten students.

Lie was appointed in 1886 to the Knights of St. Olav Order.

Family

His parents were Johann Lie, 1851 Pastor Moss on Kristianiafjord, and his wife Mette Stabell. Sophus Lie married in 1874 Anna Birk ( 1854-1920 ); she was the daughter of the Customs officials Gottfried Stenersen Jorgen Birk and his wife Marie Elisabeth Simonsen. The couple had a son Herman (1884-1960) and two daughters. Marie ( born May 21, 1877) married in 1905 the later ophthalmologist Friedrich Leskien, son of August Leskien; along with her ​​husband, she has translated works by Alexander Lange Kielland into German. Dagny Lie ( born July 5, 1880 † December 28, 1945 ) was married to the pharmacologist Walther Straub ( 1874-1944 ).

Work

Lie founded the theory of continuous symmetry, and applied them to the study of differential equations and geometric structures. Continuous or continuous symmetry operations are, for example, displacements and rotations about any, even infinitesimal amounts, in contrast to discrete symmetry operations such as reflections. On the basis of his work, an algorithm for numerical integration of differential equations has been developed, inter alia, (lie integration) or the method of foot transformation.

In order continuous transformation groups (now called Lie groups ) to investigate and apply it linearized the transformations and examined the infinitesimal generators. The association properties of the Lie group can be expressed by commutators of the generators; the commutator algebra of generators is called a Lie algebra today.