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1. Topological group: A set $ G $ on which two structures are given — a group structure and a topology, such that the group operations are continuous. Specifically, the mapping $ (a, b) \mapsto ab ^ {-1} $ from the direct product $ G \times G $ into $ G $ must ... (Mathematics) [100%] 2022-11-28
2. Topological group: A topological group is a topological space that is also a group such that the binary operation defined on the group is a continuous map, as is the operation of inversion. Every group G can be turned into a topological ... [100%] 2023-06-24 [Topology] [Algebra]...
3. Groups: This is a learning resource created for the School of Media Technology Social media has developed in several Internet features. One feature for common use is "Groups". [91%] 2024-01-06 [Media Technology] [Learning projects]...
4. Groups: The conception of an operation to be carried out on some object or set of objects underlies all mathematical science. Thus in elementary arithmetic there are the fundamental operations of the addition and the multiplication of integers; in algebra a ... [91%] 2022-09-02
5. 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) [87%] 2023-07-14 [Lie groups] [Manifolds]...
6. 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) [87%] 2023-10-17
7. Galois topological group: A Galois group endowed with the Krull topology; the filter base (i.e. a basis of the open neighbourhoods of the identity) of this topology consists of normal subgroups of finite index. (Mathematics) [81%] 2023-09-25
8. Local topological group: A topological group in which the group operations are defined only for elements sufficiently close to the identity. The introduction of local topological groups was inspired by the study of the local structure of topological groups (that is, their structure ... (Mathematics) [81%] 2023-10-22
9. Topological semi-group: A set equipped with both the algebraic structure of a semi-group and the structure of a topological Hausdorff space, such that the semi-group operation is continuous in the given topology. Any semi-group is a topological semi-group ... (Mathematics) [81%] 2023-07-18
10. Groupe (stratigraphie): Pour les articles homonymes, voir Groupe. En stratigraphie, un groupe est une unité stratigraphique faisant partie d'une strate géologique. (Stratigraphie) [74%] 2024-04-18
11. GroupM: GroupM is a U.S. based media investment group of the multinational Holding company WPP plc. (American company) [74%] 2025-03-17 [American companies established in 2003] [WPP plc]...
12. Line group: A line group is a mathematical way of describing symmetries associated with moving along a line. These symmetries include repeating along that line, making that line a one-dimensional lattice. [74%] 2023-12-04 [Euclidean symmetries] [Discrete groups]...
13. Direct sum of topological groups: In mathematics, a topological group \displaystyle{ G }[/math] is called the topological direct sum of two subgroups \displaystyle{ H_1 }[/math] and \displaystyle{ H_2 }[/math] if the map \displaystyle{ \begin{align} H_1\times H_2 &\longrightarrow G \\ (h_1,h_2) &\longmapsto h_1 h_2 ... [72%] 2024-07-25 [Topological groups] [Topology]...
14. 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 ... [72%] 2024-01-01 [Lie groups] [Lie algebras]...
15. 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 ... [72%] 2023-10-08 [Mathematics books] [Lie groups]...
16. 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) [71%] 2023-09-02 [Lie theory and generalizations]
17. 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 ... [71%] 2023-07-17 [Lie groups] [Symplectic geometry]...
18. 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) [71%] 2023-10-12 [Lie theory and generalizations]
19. 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) [71%] 2023-08-03 [Numerical analysis]
20. 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) [71%] 2023-10-18