killing form मीनिंग इन हिंदी

उदाहरण वाक्य

1. The Cartan subalgebra inherits an inner product from the Killing form on.
2. A natural inner product on \ mathfrak g is given by the Killing form.
3. The dual cone with respect to the Killing form is the maximal invariant convex cone.
4. The converse is false : there are non-nilpotent Lie algebras whose Killing form vanishes.
5. Derivations on \ mathfrak { h } are skew-adjoint for the inner product given by minus the Killing form.
6. The second one is the compact real form and its Killing form is negative definite, i . e . has signature.
7. The Killing form and the Casimir invariant also have a particularly simple form, when written in terms of the structure constants.
8. The Killing form is negative definite on the + 1 eigenspace of ? and positive definite on the  " 1 eigenspace.
9. The real forms of a given complex semisimple Lie algebra are frequently labeled by the positive index of inertia of their Killing form.
10. By Cartan's criterion, the Killing form is nondegenerate, and can be diagonalized in a suitable basis with the diagonal entries.