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...

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

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...

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...

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...

(\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...