killing form उदाहरण वाक्य

उदाहरण वाक्य

1. In particular, a real Lie algebra \ mathfrak g is called "'compact "'if the Killing form is negative definite.
2. The first one is noncompact, the so-called "'split real form "', and its Killing form has signature.
3. This set of roots form a root system inside \ mathfrak { h } ^ *, as defined above, where the inner product is the Killing form.
4. Intrinsically and algebraically, a compact Lie algebra is a real Lie algebra whose Killing form is negative definite; this definition is more restrictive and excludes tori,.
5. The special feature of a Cartan decomposition is that the Killing form is negative definite on \ mathfrak { k } and positive definite on \ mathfrak { p }.
6. When the Killing form of the Lie algebra is contracted with the current commutator, one obtains the energy-momentum tensor of a two-dimensional conformal field theory.
7. If a finite-dimensional Lie algebra is nilpotent, then the Killing form is identically zero ( and more generally the Killing form vanishes on any nilpotent ideal ).
8. If a finite-dimensional Lie algebra is nilpotent, then the Killing form is identically zero ( and more generally the Killing form vanishes on any nilpotent ideal ).
9. By Cartan's criterion, the Killing form is nondegenerate, and can be diagonalized in a suitable basis with the diagonal entries + 1 or  " 1.
10. Furthermore, \ mathfrak { k } and \ mathfrak { p } are orthogonal complements of each other with respect to the Killing form on \ mathfrak { g }.