-
Recent Posts
- Monopole and dipole dynamics on Riemann surfaces
- The Symmetries of the Quantum Kepler Problem
- The geometry of a second order differential equation, part 2
- The geometry of a second order differential equation, part 1
- The geometry of y”+y=0
- Vortex dynamics
- The Gelfand-Fuchs cocycle
- The Schwarzian derivative
- The Lie bracket is torsion
- The cross ratio
- Sample variance
- Calculating the Lie algebra of a Lie group
- The partial derivative as a quotient
- Second derivative as a quotient
- The second differential
Recent Comments
Vortex dynamics | Cu… on The Schwarzian derivative Archives
- July 2022 (1)
- January 2022 (1)
- July 2020 (3)
- January 2020 (1)
- July 2016 (1)
- September 2015 (1)
- June 2015 (1)
- May 2015 (1)
- April 2015 (2)
- March 2015 (1)
- February 2015 (1)
- January 2015 (1)
Categories
- cohomology (1)
- complex analysis (1)
- differential equations (3)
- differential geometry (3)
- Lie groups (2)
- Okategoriserade (2)
- projective geometry (5)
- statistics (1)
Tags
Meta
Category Archives: Lie groups
The Lie bracket is torsion
We start with a Lie group . An element acts on an external vector by . Let be generated by a vector at the identity , . By differentiating, with , the velocity of is This can also be interpreted … Continue reading
Posted in Lie groups
Tagged differentials, exterior derivative, Lie algebras, Lie bracket, torsion
Leave a comment
Calculating the Lie algebra of a Lie group
The Lie algebra of a Lie group is the tangent space at the identity. Thus we can compute the Lie algebra by differentiating the Lie group and evaluating the derivative at the identity. Example 1. Let . These are the … Continue reading
Curved Maths 