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1. Lie group: In mathematics, a Lie group (pronounced /liː/ LEE) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the additional ... (Group that is also a differentiable manifold with group operations that are smooth) [100%] 2023-07-14 [Lie groups] [Manifolds]...
2. Lie group: A group $ G $ having the structure of an analytic manifold such that the mapping $ \mu : \ ( x ,\ y ) \rightarrow x y ^{-1} $ of the direct product $ G \times G $ into $ G $ is analytic. In other words, a Lie group is a ... (Mathematics) [100%] 2023-10-17
3. Table of Lie groups: This article gives a table of some common Lie groups and their associated Lie algebras. The following are noted: the topological properties of the group (dimension; connectedness; compactness; the nature of the fundamental group; and whether or not they are ... [99%] 2024-01-01 [Lie groups] [Lie algebras]...
4. Theory of Lie groups: In mathematics, Theory of Lie groups is a series of books on Lie groups by Claude Chevalley (1946, 1951, 1955). The first in the series was one of the earliest books on Lie groups to treat them from the global ... [99%] 2023-10-08 [Mathematics books] [Lie groups]...
5. Lin Lie: Lin Line (林烈) es un superhéroe Chino que aparece en los cómics americanos publicados por Marvel Comics. Lin apareció por primera vez en la web manhua Warrior of the Three Sovereigns (chino simplificado: 三皇斗战士) #1 (mayo de 2018) como Sword Master, un descendiente ... [95%] 2023-11-17
6. Lin Lie: Lin Lie (Chinese: 林烈) is a Chinese superhero originally appearing in web manhua and later American comic books published by Marvel Comics. Created by artist Gunji and writer Shuizhu, Lin first appeared in the Chinese digital series Warrior of the Three ... (Fictional superhero in Marvel Comics) [95%] 2023-12-28 [Chinese superheroes] [Iron Fist (comics)]...
7. Group of Lie type: In mathematics, specifically in group theory, the phrase group of Lie type usually refers to finite groups that are closely related to the group of rational points of a reductive linear algebraic group with values in a finite field. The ... [91%] 2023-12-03 [Group theory] [Lie algebras]...
8. Representations of classical Lie groups: In mathematics, the finite-dimensional representations of the complex classical Lie groups \displaystyle{ GL(n,\mathbb{C}) }[/math], \displaystyle{ SL(n,\mathbb{C}) }[/math], \displaystyle{ O(n,\mathbb{C}) }[/math], \displaystyle{ SO(n,\mathbb{C}) }[/math], \displaystyle{ Sp(2n,\mathbb ... [88%] 2023-07-23 [Representation theory of Lie groups] [Lie groups]...
9. List of Lie groups topics: This is a list of Lie group topics, by Wikipedia page. See Table of Lie groups for a list. (Wikipedia list article) [88%] 2023-07-24 [Mathematics-related lists] [Lie groups]...
10. List of Lie groups topics: This is a list of Lie group topics, by Wikipedia page. See Table of Lie groups for a list. (none) [88%] 2023-10-30 [Mathematics-related lists] [Lie groups]...
11. Glossary of Lie groups and Lie algebras: This is a glossary for the terminology applied in the mathematical theories of Lie groups and Lie algebras. For the topics in the representation theory of Lie groups and Lie algebras, see Glossary of representation theory. (none) [87%] 2024-10-01 [Glossaries of mathematics] [Lie algebras]...
12. Rank of a Lie group: (real or complex) The (real, respectively, complex) dimension of any Cartan subgroup of it. The rank of a Lie group coincides with the rank of its Lie algebra (see Rank of a Lie algebra). (Mathematics) [81%] 2023-10-17 [Lie theory and generalizations]
13. Complexification of a Lie group: The complexification of a Lie group $G$ over $\R$ is a complex Lie group $G_\C$ containing $G$ as a real Lie subgroup such that the Lie algebra $\def\fg{ {\mathfrak g}}\fg$ of $G$ is a real form of ... (Mathematics) [81%] 2022-09-21
14. Representation of a Lie group: In mathematics and theoretical physics, a representation of a Lie group is a linear action of a Lie group on a vector space. Equivalently, a representation is a smooth homomorphism of the group into the group of invertible operators on ... (Group representation) [81%] 2024-08-14 [Representation theory of Lie groups] [Lie groups]...
15. Lie group, supersolvable: triangular Lie group A connected real Lie group $G$ for which the eigen values of the operators $\mathrm{Ad}\,g$ of adjoint representation (cf. Adjoint representation of a Lie group) are real for any element $g$. (Mathematics) [81%] 2023-09-02 [Lie theory and generalizations]
16. Poisson–Lie group: In mathematics, a Poisson–Lie group is a Poisson manifold that is also a Lie group, with the group multiplication being compatible with the Poisson algebra structure on the manifold. The infinitesimal counterpart of a Poisson–Lie group is a ... [81%] 2023-07-17 [Lie groups] [Symplectic geometry]...
17. Lie group, exponential: Lie group of type $(E)$ A real finite-dimensional Lie group $G$ for which the exponential mapping $\exp\colon \mathfrak{g} \to G$, where $\mathfrak{g}$ is the Lie algebra of $G$, is a diffeomorphism. Any exponential Lie group is ... (Mathematics) [81%] 2023-10-12 [Lie theory and generalizations]
18. Lie group integrator: A Lie group integrator is a numerical integration method for differential equations built from coordinate-independent operations such as Lie group actions on a manifold. They have been used for the animation and control of vehicles in computer graphics and ... (Method of numerical integration of partial differential equations) [81%] 2023-08-03 [Numerical analysis]
19. Lie group, Banach: A set $ G $ endowed with a group structure and an analytic Banach manifold structure (cf. Banach analytic space) at the same time; these two structures are compatible in the following sense: the mapping $ ( g , h ) \rightarrow g h ^ {-} 1 $ from ... (Mathematics) [81%] 2023-10-18
20. Lie group, solvable: A Lie group that is solvable as an abstract group (cf. Solvable group). (Mathematics) [81%] 2023-09-10