Definition:Lie Theory
Definition
Lie theory is the study of Lie groups and Lie algebras.
Also see
- Results about Lie theory can be found here.
Source of Name
This entry was named for Marius Sophus Lie.
Historical Note
The branch of mathematics now known as Lie theory emerged from the research by Marius Sophus Lie, started in $1873$, into the structure of what are now known as Lie groups.
The results of this research appeared in the publication of $3$ papers by Marius Sophus Lie and Friedrich Engel between $1888$ and $1893$, and $4$ papers by Wilhelm Karl Joseph Killing between $1888$ and $1890$.
The work built on the concepts of groups and matrices by Arthur Cayley, William Rowan Hamilton and James Joseph Sylvester, dating back to the years between $1850$ and $1859$.
More recently, Lie groups have shown they have a practical application in modern physics.