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...

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...

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

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

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 ...

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...

(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...

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

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...

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...

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...

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

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...

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

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

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

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...

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...

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

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...

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...

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}}}...

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

\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...

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...

section through that bundle. Coupled to the frame bundle is a second bundle, the spinor bundle. A section through the spinor bundle is just the particle...

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...