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1. 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". [100%] 2024-01-06 [Media Technology] [Learning projects]...
2. 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 ... [100%] 2022-09-02
3. 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) [95%] 2023-07-14 [Lie groups] [Manifolds]...
4. 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) [95%] 2023-10-17
5. Groupe (stratigraphie): Pour les articles homonymes, voir Groupe. En stratigraphie, un groupe est une unité stratigraphique faisant partie d'une strate géologique. (Stratigraphie) [81%] 2024-04-18
6. 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. [81%] 2023-12-04 [Euclidean symmetries] [Discrete groups]...
7. 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 ... [79%] 2024-01-01 [Lie groups] [Lie algebras]...
8. 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 ... [79%] 2023-10-08 [Mathematics books] [Lie groups]...
9. 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) [78%] 2023-09-02 [Lie theory and generalizations]
10. 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 ... [78%] 2023-07-17 [Lie groups] [Symplectic geometry]...
11. 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) [78%] 2023-10-12 [Lie theory and generalizations]
12. 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) [78%] 2023-08-03 [Numerical analysis]
13. 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) [78%] 2023-10-18
14. Lie group, solvable: A Lie group that is solvable as an abstract group (cf. Solvable group). (Mathematics) [78%] 2023-09-10
15. Lie transformation group: A smooth action of a connected Lie group $ G $ on a smooth manifold $ M $, that is, a smooth mapping (of class $ C ^ \infty $) $ A : G \times M \rightarrow M $ such that I) $ A ( g ^ \prime g ^ {\prime\prime} , m ) = A ... (Mathematics) [78%] 2023-08-27
16. Lie group, compact: A compact group that is a finite-dimensional real Lie group. Compact Lie groups can be characterized as finite-dimensional locally connected compact topological groups. (Mathematics) [78%] 2023-09-18
17. Lie group, nilpotent: A Lie group that is nilpotent as an abstract group (cf. Nilpotent group). (Mathematics) [78%] 2023-07-06
18. Lie group, local: local analytic group An analytic manifold $ G $ over a field $ k $ that is complete with respect to some non-trivial absolute value, which is endowed with a distinguished element $ e $( the identity), an open subset $ U \ni e $ and a ... (Mathematics) [78%] 2023-10-01
19. Lie group, derived: The commutator subgroup of a Lie group. For any Lie group $G$ its derived Lie group $[G,G]$ is a normal (not necessarily closed) Lie subgroup of $G$. (Mathematics) [78%] 2023-10-23
20. Poisson Lie group: A Lie group $ G $ with a Poisson structure $ P $ which is compatible with the group multiplication, i.e., the multiplication $ G \times G \rightarrow G $ is a Poisson mapping, where $ G \times G $ is the product Poisson manifold (cf. Poisson ... (Mathematics) [78%] 2023-10-13