Übersetzung für 'Killing-Form' von Englisch nach Deutsch

Killing form

Killing-Form {f}math.

• on the Lie group is the Cartan metric, aka the Killing form.
• Conversely, it follows easily from Cartan's criterion for solvability that a semisimple algebra (in characteristic 0) has a non-degenerate Killing form.
• The Riemannian metric of the target manifold is given by a positive constant multiplied by the Killing form acting upon the Maurer–Cartan form of SU("N").
• 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.
• Since for a simple Lie algebra every invariant bilinear form is a multiple of the Killing form, the corresponding Casimir element is uniquely defined up to a constant.

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• The inner product [...] is the restriction of the Killing form to the Cartan subalgebra.
• A real form is called a compact form if the Killing form on it is negative-definite; it is necessarily the Lie algebra of a compact Lie group (hence, the name).
• The Killing form was essentially introduced into Lie algebra theory by [...] in his thesis.
• is the Killing form. The minus sign appears because the Killing form is negative-definite on [...] this makes [...] positive-definite.
• The metric tensor [...] on the Lie group is the Cartan metric, the Killing form. For [...] a (pseudo-)Riemannian manifold, the metric is a (pseudo-)Riemannian metric.

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• These arise in particular when [...] above is semisimple, when the Killing form provides a duality between [...] and [...].