mathematics, an adjoint bundle is a vector bundle naturally associated with any smooth principal bundle. The fibers of the adjoint bundle carry a Lie algebra...

with any tensorial forms on P {\displaystyle P} of adjoint type. Maurer–Cartan form Adjoint bundle S. Kobayashi, K. Nomizu. Foundations of Differential...

The Lie algebra adjoint bundle is usually denoted ad ⁡ ( P ) {\displaystyle \operatorname {ad} (P)} , and the Lie group adjoint bundle by Ad ⁡ ( P ) {\displaystyle...

In mathematics, the adjoint representation (or adjoint action) of a Lie group G is a way of representing the elements of the group as linear transformations...

connection, and a Higgs field, given by a section of a vector bundle (specifically, the adjoint bundle). These equations are D A ∗ F A + ∗ [ Φ , D A Φ ] = 0 ...

(mathematics), a connection over a principal bundle G with a section (the Higgs field) of the associated adjoint bundle Monopole, the first term in a multipole...

section of the vertical bundle V of P. Hence it is basic and so is determined by a 1-form on M with values in the adjoint bundle g P := P × G g . {\displaystyle...

self-adjoint operator is an operator equal to its own (formal) adjoint. If Ω is a domain in Rn, and P a differential operator on Ω, then the adjoint of...

{C} )} there is still a natural associated vector bundle to P {\displaystyle P} , the adjoint bundle ad ⁡ P {\displaystyle \operatorname {ad} P} , with...

capital A adjoint bundle Ad ⁡ ( F ( E ) ) {\displaystyle \operatorname {Ad} ({\mathcal {F}}(E))} of the frame bundle of the vector bundle E {\displaystyle...

this relationship are known as adjoint functors, one being the left adjoint and the other the right adjoint. Pairs of adjoint functors are ubiquitous in mathematics...

bundle. This connection has a curvature form F A {\displaystyle F_{A}} , which is a two-form on X {\displaystyle X} with values in the adjoint bundle...

field on the spacetime with values in the adjoint bundle of the chromodynamical SU(3) gauge group (see vector bundle for necessary definitions). Throughout...

mathematics, a monopole is a connection over a principal bundle G with a section of the associated adjoint bundle. Physically, the section can be interpreted as...

{\displaystyle G} -bundle over a 3-manifold M {\displaystyle M} , Φ {\displaystyle \Phi } is a section of the corresponding adjoint bundle, d A {\displaystyle...

difference of two adapted connections is a 1-form on M with values in the adjoint bundle AdQ. That is to say, the space AQ of adapted connections is an affine...

resulting in an isomorphism between the transpose and adjoint of u. The matrix of the adjoint of a map is the transposed matrix only if the bases are...

MR 1207013. Fujita, Takao (1987), "On polarized manifolds whose adjoint bundles are not semipositive", Algebraic geometry, Sendai, 1985, Adv. Stud...

are implemented for G-invariant self-adjoint operators between vector bundles associated to some principal G-bundle, although the precise conditions under...

1-forms, where ad ( P ) {\displaystyle {\text{ad}}(P)} is the associated adjoint bundle. For any non-empty subset X of an affine space A, there is a smallest...

vertical bundle and the horizontal bundle are vector bundles associated to a smooth fiber bundle. More precisely, given a smooth fiber bundle π : E → B...

\operatorname {Ad} (E):=E\times _{G}{\mathfrak {g}}\twoheadrightarrow B} be its adjoint bundle. Ω Ad 1 ( E , g ) ≅ Ω 1 ( B , Ad ⁡ ( E ) ) {\displaystyle \Omega _{\operatorname...

Lie group bundle over the same base space whose Lie algebra bundle is isomorphic to the given Lie algebra bundle. Algebra bundle Adjoint bundle A. Weinstein...

{\displaystyle {\text{ad}}P^{\mathbb {C} }} is the complexification of the adjoint bundle of P {\displaystyle P} , with fibre given by the complexification g...

Yang–Mills gauge theory of principal connections on a principal bundle. Given a principal bundle P → X {\displaystyle P\to X} with a structure Lie group G {\displaystyle...

of adjoint type. The "difference" of two connection forms is a tensorial form. Given P and ρ as above one can construct the associated vector bundle E...

given magnitude Einstein–Hermitian vector bundle Deformed Hermitian Yang–Mills equation Hermitian adjoint Hermitian connection, the unique connection...

on P {\displaystyle P} , its isotropy Lie algebra bundle is isomorphic to the adjoint vector bundle P × G g {\displaystyle P\times _{G}{\mathfrak {g}}}...

reflective in B when the inclusion functor from A to B has a left adjoint.: 91  This adjoint is sometimes called a reflector, or localization. Dually, A is...

of PU. The adjoint action of the infinite projective unitary group is useful in geometric definitions of twisted K-theory. Here the adjoint action of the...