Killing form

In mathematics, the Killing form, called afterwards Wilhelm Killing, is a symmetric bilinear anatomy that plays a basal role in the theori...

Consider a Lie algebra g over a acreage K. Every aspect x of g defines the adjoint endomorphism ad(x) (also accounting as adx) of g with the...

The Killing anatomy B is bilinear and symmetric. The Killing anatomy is an invariant form, in the faculty that it has the 'associativi...

Given a basis ei of the Lie algebra g, the matrix elements of the Killing form are given by     B^{ij}= tr (\textrm{ad}(e^i)\circ \textrm{...

Suppose that g is a semisimple Lie algebra over the acreage of absolute numbers. By Cartan's criterion, the Killing anatomy is nondegene...