In mathematics, the Killing form, named after Wilhelm Killing, is a symmetric bilinear form that plays a basic role in the theories of Lie groups and...

Look up killing in Wiktionary, the free dictionary. Killing, Killings, or The Killing may refer to: -cide, a suffix that refers to types of killing (see...

second fundamental form), differential topology (intersection forms of manifolds, especially four-manifolds), Lie theory (the Killing form), and statistics...

are equivalent: g {\displaystyle {\mathfrak {g}}} is semisimple; the Killing form, κ(x,y) = tr(ad(x)ad(y)), is non-degenerate; g {\displaystyle {\mathfrak...

In mathematics, a Killing vector field (often called a Killing field), named after Wilhelm Killing, is a vector field on a Riemannian manifold (or pseudo-Riemannian...

Contract killing (also known as murder-for-hire) is a form of murder or assassination in which one party hires another party to kill a targeted person...

its Killing form is negative definite (making it a compact Lie algebra), and that the complexification of u0 is g. Therefore, u0 is a compact form of g...

⋅ | ⋅ ⟩ {\displaystyle \langle \cdot |\cdot \rangle } is the Cartan-Killing form on g . {\displaystyle {\mathfrak {g}}.} The affine Lie algebra corresponding...

A Higher Form of Killing is the second studio album by the metal band, Intruder. It marks their departure from the speed metal sound displayed on their...

(\operatorname {ad} X\circ \operatorname {ad} Y)} is the Killing form. The minus sign appears because the Killing form is negative-definite on h   ; {\displaystyle...

context of Lie algebras were first investigated by Wilhelm Killing, whereas the Killing form is due to Cartan.[citation needed] A (symmetrizable) generalized...

\mathbf {X} } is called the Killing form, which is used for the classification of Lie algebras. The trace defines a bilinear form: ( X , Y ) ↦ tr ⁡ ( X Y...

1007/bf01207841. S2CID 121548146. Killing equation Killing form Killing–Hopf theorem Killing horizon Killing spinor Killing tensor Killing vector field Levi decomposition...

killing children. Senicide or geronticide – the act of killing an elderly person. Targeted killing – a form of assassination which is carried out by governments...

and algebraically, a compact Lie algebra is a real Lie algebra whose Killing form is negative definite; this definition is more restrictive and excludes...

An honor killing (American English), honour killing (Commonwealth English), or shame killing is a traditional form of murder in which a person is killed...

Killing Eve is a British spy thriller television series, produced in the United Kingdom by Sid Gentle Films for BBC America and BBC Three. The series...

Targeted killing is a form of assassination carried out by governments outside a judicial procedure or a battlefield. Since the late 20th century, the...

solvable or semisimple. It is expressed in terms of the Killing form, the symmetric bilinear form on g {\displaystyle {\mathfrak {g}}} defined by K ( u...

intentionally kills one or more people before killing themselves. The combination of murder and suicide can take various forms: Suicide after or during murder inflicted...

elements of g {\displaystyle {\mathfrak {g}}} are ad-nilpotent. The Killing form of a nilpotent Lie algebra is 0. A nonzero nilpotent Lie algebra has...

On Killing: The Psychological Cost of Learning to Kill in War and Society is a book by Dave Grossman exploring the psychology of the act of killing and...

Λ) such that R is a ring and Λ a form parameter is called form ring. Let M be an R-module and f a J-sesquilinear form on M (i.e., f ( x r , y s ) = r J...

An extrajudicial killing (also known as an extrajudicial execution or an extralegal killing) is the deliberate killing of a person without the lawful...

The Killing Of A Sacred Deer is a 2017 absurdist psychological horror thriller film directed and co-produced by Yorgos Lanthimos, who also co-wrote the...

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...

In mathematics, a Killing tensor or Killing tensor field is a generalization of a Killing vector, for symmetric tensor fields instead of just vector fields...

are Killing vector fields which are those spacetime symmetries that preserve the underlying metric structure of a manifold. In rough terms, Killing vector...

Killing Joke are an English rock band formed in Cheltenham, Gloucestershire, in 1979 by Jaz Coleman (vocals, keyboards), Paul Ferguson (drums), Geordie...

nondegenerate bilinear form over g {\displaystyle {\mathfrak {g}}} (if G is semisimple, the Killing form will do) and F is the curvature form F ≡ d A + A ∧ A...