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  1. Homogeneous space: In mathematics, particularly in the theories of Lie groups, algebraic groups and topological groups, a homogeneous space for a group G is a non-empty manifold or topological space X on which G acts transitively. The elements of G are ... (Topological space in group theory) [100%] 2023-03-30 [Topological groups] [Lie groups]...
  2. Homogeneous space: h0476901.png 132 0 132 A set together with a given transitive group action. More precisely, $ M $ is a homogeneous space with group $ G $ if a mapping$$ ( g ,\ x ) \rightarrow g x $$ of the set $ G \times M $ into $ M ... (Mathematics) [100%] 2023-07-09
  3. Homogeneous (large cardinal property): In set theory and in the context of a large cardinal property, a subset, S, of D is homogeneous for a function f if f is constant in finite subsets of S. More precisely, given a set D, let \displaystyle ... (Large cardinal property) [92%] 2024-12-14 [Large cardinals]
  4. Algebraic algebra: An algebra with associative powers (in particular, an associative algebra) over a field in which all elements are algebraic: an element $a$ of the algebra $A$ is called algebraic over the field $F$ if the subalgebra $F$ generated by $a ... (Mathematics) [87%] 2023-10-13
  5. Homogeneous space of an algebraic group: An algebraic variety $ M $ together with a regular transitive action of an algebraic group $ G $ given on it. If $ x \in M $ , then the isotropy group $ G _{x} $ is closed in $ G $. (Mathematics) [87%] 2023-10-17
  6. Algebraic space: In mathematics, algebraic spaces form a generalization of the schemes of algebraic geometry, introduced by Michael Artin({{{1}}}, {{{2}}}) for use in deformation theory. Intuitively, schemes are given by gluing together affine schemes using the Zariski topology, while algebraic spaces ... [85%] 2022-09-26 [Algebraic geometry]
  7. Algebraic space: A generalization of the concepts of a scheme and an algebraic variety. This generalization is the result of certain constructions in algebraic geometry: Hilbert schemes, Picard schemes, moduli varieties, contractions, which are often not realizable in the category of schemes ... (Mathematics) [85%] 2023-10-17
  8. Symplectic homogeneous space: A symplectic manifold $ ( M, \omega ) $ together with a transitive Lie group $ G $ of automorphisms of $ M $. The elements of the Lie algebra $ \mathfrak g $ of $ G $ can be regarded as symplectic vector fields on $ M $, i.e. (Mathematics) [81%] 2023-10-25
  9. Riemannian space, homogeneous: A Riemannian space $ ( M, \gamma ) $ together with a transitive effective group $ G $ of motions (cf. Motion) on it. (Mathematics) [81%] 2023-09-28
  10. Quantum homogeneous space: A unital algebra $A$ that is a co-module for a quantum group $\operatorname{Fun}_{q}(G)$ (cf. Quantum groups) and for which the structure mapping $L : A \rightarrow \operatorname { Fun }_{q} (G) \otimes A$ is an algebra ... (Mathematics) [81%] 2023-12-03
  11. Principal homogeneous space: A principal $ G $- object in the category of algebraic varieties or schemes. If $ S $ is a scheme and $ \Gamma $ is a group scheme over $ S $, then a principal $ G $- object in the category of schemes over $ \Gamma $ is said to ... (Mathematics) [81%] 2023-10-11
  12. Principal homogeneous space: In mathematics, a principal homogeneous space, or torsor, for a group G is a homogeneous space X for G in which the stabilizer subgroup of every point is trivial. Equivalently, a principal homogeneous space for a group G is a ... [81%] 2024-02-18 [Group theory] [Topological groups]...
  13. Lie algebra, algebraic: The Lie algebra of an algebraic subgroup (see Algebraic group) of the general linear group of all automorphisms of a finite-dimensional vector space $V$ over a field $k$. If $\mathfrak g$ is an arbitrary subalgebra of the Lie algebra ... (Mathematics) [71%] 2023-10-17
  14. Piecewise algebraic space: In mathematics, a piecewise algebraic space is a generalization of a semialgebraic set, introduced by Maxim Kontsevich and Yan Soibelman. The motivation was for the proof of Deligne's conjecture on Hochschild cohomology. (Generalization of a semialgebraic set) [70%] 2023-11-02 [Algebraic geometry]
  15. Homogeneous coordinates: Coordinates having the property that the object determined by them does not change if all the coordinates are multiplied by the same non-zero number. Such, for example, are projective coordinates; Plücker coordinates and pentaspherical coordinates. (Mathematics) [65%] 2023-10-17
  16. Homogeneous graph: In mathematics, a k-ultrahomogeneous graph is a graph in which every isomorphism between two of its induced subgraphs of at most k vertices can be extended to an automorphism of the whole graph. A k-homogeneous graph obeys a ... [65%] 2022-07-20 [Graph families]
  17. Homogeneous coordinates: In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcul, are a system of coordinates used in projective geometry, just as Cartesian coordinates are used in Euclidean geometry. They have the ... (Coordinate system used in projective geometry) [65%] 2022-06-25 [Linear algebra] [Projective geometry]...
  18. Homogeneous polynomial: In mathematics, a homogeneous polynomial, sometimes called quantic in older texts, is a polynomial whose nonzero terms all have the same degree. For example, \displaystyle{ x^5 + 2 x^3 y^2 + 9 x y^4 }[/math] is a homogeneous ... (Polynomial whose all nonzero terms have the same degree) [65%] 2022-09-20 [Homogeneous polynomials] [Multilinear algebra]...
  19. Homogeneous Serbia: Homogeneous Serbia is a written discourse by Stevan Moljević. The work emphasized that the state drew its strength from the degree to which its population identifies itself within the state, contrary to the presumptions of Ilija Garašanin, who believed that the ... (Discourse by Stevan Moljević advocating for Greater Serbia) [65%] 2023-12-10 [1941 documents] [1941 in Yugoslavia]...
  20. Homogeneous relation: In mathematics, a homogeneous relation (also called endorelation) on a set X is a binary relation between X and itself, i.e. it is a subset of the Cartesian product X × X. (Binary relation over a set and itself) [65%] 2023-11-16 [Binary relations]

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