In mathematics, an adjoint bundle[1] is a vector bundle naturally associated to any principal bundle. The fibers of the adjoint bundle carry a Lie algebra structure making the adjoint bundle into a (nonassociative) algebra bundle. Adjoint bundles have important applications in the theory of connections as well as in gauge theory.
In mathematics, an adjointbundle is a vector bundle naturally associated to any principal bundle. The fibers of the adjointbundle 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...
field on the spacetime with values in the adjointbundle of the chromodynamical SU(3) gauge group (see vector bundle for necessary definitions). Throughout...
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...
(mathematics), a connection over a principal bundle G with a section (the Higgs field) of the associated adjointbundle Monopole, the first term in a multipole...
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 adjointbundle ad P {\displaystyle \operatorname {ad} P} , with...
{\displaystyle G} -bundle over a 3-manifold M {\displaystyle M} , Φ {\displaystyle \Phi } is a section of the corresponding adjointbundle, d A {\displaystyle...
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...
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...
1-forms, where ad ( P ) {\displaystyle {\text{ad}}(P)} is the associated adjointbundle. For any non-empty subset X of an affine space A, there is a smallest...
Lie group bundle over the same base space whose Lie algebra bundle is isomorphic to the given Lie algebra bundle. Algebra bundleAdjointbundle A. Weinstein...
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...
G} , its quotient by the diagonal G {\displaystyle G} action is the adjointbundle P × G g {\displaystyle P\times _{G}{\mathfrak {g}}} . In conclusion...
linear operator, and is known as the transpose or composition operator. Its adjoint is the push-forward, or, in the context of functional analysis, the transfer...
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}}}...
Global Information