Tag Archives: Lie algebras

The Gelfand-Fuchs cocycle

Posted on 10 July, 2016 by jesperg

Let be a vector field on the Euclidean line . Expressed in a coordinate the vector field is . The logarithm of the component value at each point of the vector field is the fundamental Euclidean invariant We now let … Continue reading →

Posted in cohomology | Tagged , , , | Leave a comment

The Lie bracket is torsion

Posted on 20 June, 2015 by jesperg

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 , , , , | Leave a comment

Calculating the Lie algebra of a Lie group

Posted on 6 April, 2015 by jesperg

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 →

Posted in Lie groups | Tagged | Leave a comment