nLab Sophus Lie

Marius Sophus Lie (1842–1899) was a pioneer of study of (and almost solely devoted to) the groups of continuous and smooth transformations, mainly motivated by symmetries of differential equations. He is the founder of the theory of Lie groups and Lie algebras, whose global theory however has been completed only with works of Élie Cartan.

• Wikipedia entry

Selected writings

On partial differential equations:

• Sophus Lie: Allgemeine Theorie der partiellen Differentialgleichungen erster Ordnung, Math. Ann. 9 (1876) 245–296

On “transformation groups”, that would come to be called Lie groups:

• Sophus Lie: Theorie der Transformationsgruppen I, Math. Ann. 16 (1880) 441–528 [doi:10.1007/BF01446218]

• Sophus Lie unter Mitwirkung von Friedrich Engel: Theorie der Transformationsgruppen, Teubner (1888) [ark:/13960/t25b0068w]

English translation:

• Joël Merker (ed.) Theory of Transformation Groups by Sophus Lie and Friedrich Engel (Vol. I 1888), Springer (2015) [doi:10.1007/978-3-662-46211-9, arXiv:1003.3202]

Related entries

• Lie's three theorems

• Lie theory

• Lie groupoid

• synthetic mathematics

  analytic versus synthetic

  synthetic differential geometry

category: people