In differential geometry, the isotropy representation is a natural linear representation of a Lie group, that is acting on a manifold, on the tangent space...

Isotropy group An isotropy group is the group of isomorphisms from any object to itself in a groupoid.[dubious – discuss] An isotropy representation is...

{\displaystyle {\mathfrak {g}}} . Succinctly, an adjoint representation is an isotropy representation associated to the conjugation action of G around the...

properties that are symmetric about an axis that is normal to a plane of isotropy. This transverse plane has infinite planes of symmetry and thus, within...

irreducible symmetric space G / K is quaternion-Kähler if and only if isotropy representation of K contains an Sp(1) summand acting like the unit quaternions...

number of modulus 1, this gives the U(1) factor of the isotropy group. The other part of the isotropy group is parametrized by the unitary matrices on the...

follows from his classification that such a representation has the same orbits as the isotropy representation of a symmetric space. Berndt, J; Olmos, C;...

in X, the stabilizer subgroup of G with respect to x (also called the isotropy group or little group) is the set of all elements in G that fix x: G x...

M_{G}} . Hamiltonian group action Equivariant differential form Isotropy representation Palais, Richard S. (1957). "A global formulation of the Lie theory...

the finite sizes of atoms and bonding considerations ensure that true isotropy of atomic position will not exist in the solid state, it is possible for...

{\displaystyle X} . Assume furthermore that the weights of the isotropy representation of U ( 1 ) {\displaystyle U(1)} on the normal bundle N X Z {\displaystyle...

(homogeneity) linear momentum p rotation in space (isotropy) angular momentum L = r × p Lorentz-boost (isotropy) boost 3-vector N = tp − Er Discrete symmetry...

the isotropy subgroup of any point acts as the identity on its entire orbit. Thus, in case the action is transitive, the normal core of any isotropy subgroup...

{\displaystyle {\mathfrak {g}}_{x}(A)=\ker(\rho _{x})} is a Lie algebra, called the isotropy Lie algebra at x {\displaystyle x} the kernel g ( A ) = ker ⁡ ( ρ ) {\displaystyle...

groups appearing, the lists present the Lie algebra of the isotropy group rather than the isotropy group itself. Here Λ3 0C6 ≅ C14 denotes the space of 3-forms...

an isomorphism of k v {\displaystyle k_{v}} -algebras. If we take the isotropy subgroup of G {\displaystyle G} for the valuation class w {\displaystyle...

every x in X, we define the stabilizer subgroup of x (also called the isotropy group or little group) as the set of all elements in G that fix x: G x...

The Mercator projection is conformal. One implication of that is the "isotropy of scale factors", which means that the point scale factor is independent...

xi in Xi creates an isomorphism G/Gi → Xi, where Gi is the stabilizer (isotropy) subgroup of G at xi. A different choice of representative yi in Xi gives...

a requirement of every truly fundamental law (due to the assumption of isotropy of space), and where the same symmetry, when present, is a simplifying...

. Of course, any fibre E x {\displaystyle E_{x}} becomes a representation of the isotropy group G x {\displaystyle G_{x}} . More generally, representations...

anisotropy, both of them are called transverse isotropy (it is called transverse isotropy because there is isotropy in either the horizontal or vertical plane)...

∈ H , {\displaystyle z\in \mathbb {H} ,} then g = e. The stabilizer or isotropy subgroup of an element z ∈ H {\displaystyle z\in \mathbb {H} } is the set...

that space is continuous, homogeneous, isotropic, and without boundaries. Isotropy is guaranteed by the fourth postulate, that all right angles are equal...

algebras. The last row and column here are the orthogonal algebra part of the isotropy algebra in the symmetric decomposition of the exceptional Lie algebras...

on h {\displaystyle {\mathfrak {h}}} , invariant under the adjoint representation and σ, induces a Riemannian structure on H / K, with H acting by isometries...

authors. The isotropy Lie algebra of a Poisson manifold ( M , π ) {\displaystyle (M,\pi )} at a point x ∈ M {\displaystyle x\in M} is the isotropy Lie algebra...

proportional. Materials can have varying extents of linearity, homogeneity and isotropy. The invariance of the form of Maxwell's equations under Lorentz transformation...

isometries that leave the origin fixed. Thus, the Lorentz group is the isotropy subgroup with respect to the origin of the isometry group of Minkowski...

which is just the isotropy subgroup at x {\displaystyle x} for the given action (which is why vertex groups are also called isotropy groups). Similarly...