Sentence examples for be a connected Lie from inspiring English sources

Let G be a connected Lie group with the Lie algebra G.

for a bi-invariant Riemannian metric on G. Let G be a connected Lie group.

Let G be a connected Lie group with Lie algebra g = T e G Open image in new window.

[4] Let G be a connected Lie group with Lie algebra g Open image in new window, and let F be a left-invariant Finsler metric on G. Then X ∈ g − { 0 } Open image in new window is a geodesic vector if and only if: g X ( X, [ X, Z ] ) = 0 Open image in new window.

Let G be a connected Lie group, g = T e G Open image in new window its Lie algebra identified with the tangent space at the identity element, F ~ : g → R + Open image in new window a Minkowski norm and F the left-invariant Finsler metric induced by F ~ Open image in new window on G.

This property implies that (sigma ) is an involution (i.e., it has order 2), and that (Aut ({mathcal {D}})^0) (the connected component of the identity) is transitive on ({mathcal {D}}), and one can write ({mathcal {D}}= G/K ), where G is a connected Lie group, and K is a maximal compact subgroup.

Let G be a connected, simply connected Lie group and let g be its algebra.

Let G be a connected semisimple Lie group with finite center,G0 its Lie algebra.

Let G be a connected semisimple Lie group with no compact factors and finite center and Γ ⊂ G an irreducible lattice.

Let G be a connected semisimple Lie group with finite center, and suppose G contains a compact Cartan subgroup T. Certain irreducible unitary representations of G arise as spaces of harmonic forms associated to Dolbeault cohomology of line bundles over the complex homogeneous space G/T.

Let G be a connected 1-D Lie group and a Lie group homomorphism.