. . . "\uB9AC \uB300\uC751"@ko . . . "43302095"^^ . . "Lie_algebra_of_an_analytic_group&oldid=13500"@en . . . "\uB9AC \uAD70\uB860\uC5D0\uC11C \uB9AC \uB300\uC751(Lie\u5C0D\u61C9, \uC601\uC5B4: Lie correspondence)\uC740 \uB9AC \uAD70\uC758 \uBC94\uC8FC\uC5D0\uC11C \uC2E4\uC218 \uB9AC \uB300\uC218\uC758 \uBC94\uC8FC\uB85C \uAC00\uB294 \uD45C\uC900\uC801\uC778 \uD568\uC790\uC774\uB2E4. \uC989, \uAC01 \uB9AC \uAD70\uC5D0 \uD45C\uC900\uC801 \uC2E4\uC218 \uB9AC \uB300\uC218\uAC00 \uB300\uC751\uB418\uBA70, \uB9AC \uAD70\uC758 \uB9E4\uB044\uB7EC\uC6B4 \uAD70 \uC900\uB3D9\uD615\uC5D0 \uC2E4\uC218 \uB9AC \uB300\uC218\uC758 \uC900\uB3D9\uD615\uC774 \uB300\uC751\uB41C\uB2E4."@ko . . . . . . . . . "27163"^^ . . . . . . . . . . . . "In mathematics, Lie group\u2013Lie algebra correspondence allows one to correspond a Lie group to a Lie algebra or vice versa, and study the conditions for such a relationship. Lie groups that are isomorphic to each other have Lie algebras that are isomorphic to each other, but the converse is not necessarily true. One obvious counterexample is and (see real coordinate space and the circle group respectively) which are non-isomorphic to each other as Lie groups but their Lie algebras are isomorphic to each other. However, by restricting our attention to the simply connected Lie groups, the Lie group-Lie algebra correspondence will be one-to-one. In this article, a Lie group refers to a real Lie group. For the complex and p-adic cases, see complex Lie group and p-adic Lie group. In this article, manifolds (in particular Lie groups) are assumed to be second countable; in particular, they have at most countably many connected components."@en . "Popov"@en . . . . . . . . . . "1111909962"^^ . . . . . . . . . . . . . "V.L."@en . . "En matem\u00E1ticas, la correspondencia entre el grupo de Lie y el \u00E1lgebra de Lie permite estudiar los grupos de Lie, que son objetos geom\u00E9tricos, en t\u00E9rminos de \u00E1lgebras de Lie, que son objetos lineales. En este art\u00EDculo, cuando se habla de un grupo de Lie se hace referencia a un grupo de Lie real. Para los casos complejos y p-\u00E1dicos, v\u00E9ase el grupo de Lie complejo y el grupo de Lie p-\u00E1dico. En este art\u00EDculo, se supone que las variedades (en particular, los grupos de Lie) son los segundos numerables; en particular, tienen como m\u00E1ximo varios componentes conectados."@es . . . . . . . . . . . . "Lie group\u2013Lie algebra correspondence"@en . . . . "En matem\u00E1ticas, la correspondencia entre el grupo de Lie y el \u00E1lgebra de Lie permite estudiar los grupos de Lie, que son objetos geom\u00E9tricos, en t\u00E9rminos de \u00E1lgebras de Lie, que son objetos lineales. En este art\u00EDculo, cuando se habla de un grupo de Lie se hace referencia a un grupo de Lie real. Para los casos complejos y p-\u00E1dicos, v\u00E9ase el grupo de Lie complejo y el grupo de Lie p-\u00E1dico. En este art\u00EDculo, se supone que las variedades (en particular, los grupos de Lie) son los segundos numerables; en particular, tienen como m\u00E1ximo varios componentes conectados."@es . . . . . . . . . . . . . "Correspondencia grupo de Lie-\u00E1lgebra de Lie"@es . . . . . . . . . "Lie algebra of an analytic group"@en . . . . . . . . "\uB9AC \uAD70\uB860\uC5D0\uC11C \uB9AC \uB300\uC751(Lie\u5C0D\u61C9, \uC601\uC5B4: Lie correspondence)\uC740 \uB9AC \uAD70\uC758 \uBC94\uC8FC\uC5D0\uC11C \uC2E4\uC218 \uB9AC \uB300\uC218\uC758 \uBC94\uC8FC\uB85C \uAC00\uB294 \uD45C\uC900\uC801\uC778 \uD568\uC790\uC774\uB2E4. \uC989, \uAC01 \uB9AC \uAD70\uC5D0 \uD45C\uC900\uC801 \uC2E4\uC218 \uB9AC \uB300\uC218\uAC00 \uB300\uC751\uB418\uBA70, \uB9AC \uAD70\uC758 \uB9E4\uB044\uB7EC\uC6B4 \uAD70 \uC900\uB3D9\uD615\uC5D0 \uC2E4\uC218 \uB9AC \uB300\uC218\uC758 \uC900\uB3D9\uD615\uC774 \uB300\uC751\uB41C\uB2E4."@ko . . . . . . . . . "In mathematics, Lie group\u2013Lie algebra correspondence allows one to correspond a Lie group to a Lie algebra or vice versa, and study the conditions for such a relationship. Lie groups that are isomorphic to each other have Lie algebras that are isomorphic to each other, but the converse is not necessarily true. One obvious counterexample is and (see real coordinate space and the circle group respectively) which are non-isomorphic to each other as Lie groups but their Lie algebras are isomorphic to each other. However, by restricting our attention to the simply connected Lie groups, the Lie group-Lie algebra correspondence will be one-to-one."@en . . . . . . .