killing form वाक्य
उदाहरण वाक्य
मोबाइल
- The Cartan subalgebra inherits an inner product from the Killing form on.
- A natural inner product on \ mathfrak g is given by the Killing form.
- The dual cone with respect to the Killing form is the maximal invariant convex cone.
- The converse is false : there are non-nilpotent Lie algebras whose Killing form vanishes.
- Derivations on \ mathfrak { h } are skew-adjoint for the inner product given by minus the Killing form.
- The second one is the compact real form and its Killing form is negative definite, i . e . has signature.
- The Killing form and the Casimir invariant also have a particularly simple form, when written in terms of the structure constants.
- The Killing form is negative definite on the + 1 eigenspace of ? and positive definite on the " 1 eigenspace.
- The real forms of a given complex semisimple Lie algebra are frequently labeled by the positive index of inertia of their Killing form.
- By Cartan's criterion, the Killing form is nondegenerate, and can be diagonalized in a suitable basis with the diagonal entries.
- In particular, a real Lie algebra \ mathfrak g is called "'compact "'if the Killing form is negative definite.
- The first one is noncompact, the so-called "'split real form "', and its Killing form has signature.
- This set of roots form a root system inside \ mathfrak { h } ^ *, as defined above, where the inner product is the Killing form.
- 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,.
- The special feature of a Cartan decomposition is that the Killing form is negative definite on \ mathfrak { k } and positive definite on \ mathfrak { p }.
- 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.
- 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 ).
- 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 ).
- By Cartan's criterion, the Killing form is nondegenerate, and can be diagonalized in a suitable basis with the diagonal entries + 1 or " 1.
- Furthermore, \ mathfrak { k } and \ mathfrak { p } are orthogonal complements of each other with respect to the Killing form on \ mathfrak { g }.
- अधिक वाक्य: 1 2
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