Explore: Transformation Lie

infinitesimal transformations was first given by Sophus Lie. This was at the heart of his work, on what are now called Lie groups and their accompanying Lie algebras;

Lie's principal tool, and one of his greatest achievements, was the discovery that continuous transformation groups (now called, after him, Lie groups)

In mathematics, Bäcklund transforms or Bäcklund transformations (named after the Swedish mathematician Albert Victor Bäcklund) relate partial differential

to be called Lie theory. For instance, the latter subject is Lie sphere geometry. This article addresses his approach to transformation groups, which

In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that

distances between points lying on a straight line. If X is the point set of an affine space, then every affine transformation on X can be represented as

the Lie quadric (a quadric hypersurface in projective space). Lie sphere geometry is the geometry of the Lie quadric and the Lie transformations which

Affine Lie algebra Loop algebra Graded Lie algebra One-parameter group, One-parameter subgroup Matrix exponential Infinitesimal transformation Lie's third

origins. Lie groups are named after Norwegian mathematician Sophus Lie (1842–1899), who laid the foundations of the theory of continuous transformation groups

is an orthogonal transformation. As a Lie group, the group of Galilean transformations has dimension 10. Two Galilean transformations G(R, v, a, s) and