Borel subgroup
Borel subgroup In the theory of algebraic groups, a Borel subgroup of an algebraic group G is a ... maximal Zariski closed and connected solvable algebraic subgroup. For example, in the group GL n (n x n invertible matrices), the subgroup of upper triangular matrices is a Borel subgroup. For groups realized over algebraically closed ...
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Talk:Borel subgroup
Talk:Borel subgroup This article is not helpful at all in explaining why "parabolic" subgroups are called as such. %0?è�á ... particular the notion of Borel and minimal parabolic can diverge and the latter can take ...
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Möbius transformation
... of every Riemann surface is a discrete subgroup of the Möbius group (see Fuchsian group ... of hyperbolic 3-manifolds. A particularly important subgroup of the Möbius group is the modular ... transformations are commonly classified into four types, parabolic, elliptic, hyperbolic and loxodromic (actually hyperbolic is ... det{\mathfrak{H}}=ad-bc=1 . Parabolic transforms The transform is said to be parabolic if $\backslash mbox\{tr\}^2\backslash mathfrak\{\; ...$
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Lorentz group
... Basic properties The Lorentz group is a subgroup of the Poincaré group, the group of ... Thus, the Lorentz group is an isotropy subgroup of the isometry group of Minkowski spacetime ... improper Lorentz transformations have determinant −1.) The subgroup of proper Lorentz transformations is denoted SO(1,3). The subgroup of orthochronous transformations is often denoted O ... SO + (1, 3). It is a normal subgroup of the Lorentz group which is ...
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Talk:Riemann surface
... right? C is simply connected noncompact and parabolic, and C mod some rank 2 discrete lattice group is closed parabolic, which is not simply connected (pi1 = lattice ... something along these lines: "For every closed parabolic Riemann surface, the fundamental group is isomorphic ... says pi1 of universal cover mod discrete subgroup = discrete subgroup. Last I looked, Riemann sphere was ...
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Glossario of theory of the groups   (translated from Italian)
... 每tutti i periodi dei suoi elementi 。 Subgroup of a group (G, *) Sottoinsieme of a ... the subgroups of G containing S. Normal subgroup of a group (G,*). Subgroup H of G such that for all ... group codominio of the omomorfismo. Every normal subgroup of a group is the nucleus of ... the nucleus of every omomorfismo is normal subgroup of the group dominion. Isomorfismo between ...
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Talk:Möbius transformation
... flow lines for typical elliptic, hyperbolic, loxodromic, parabolic transformations. I like the fact that the ... the coset space of the four dimensional subgroup of similitudes on the euclidean plane, which ... the coset space of the three dimensional subgroup E(2), the isometry group of the ... stabilizer of a null vector is a subgroup of the stabilizer of a null line ... the coset space of the three dimensional subgroup SO(3), which is the stabilizer ...
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List of mathematics articles (P-R)
... truncated dodecahedron -- Parabidiminished rhombicosidodecahedron -- Parabigyrate rhombicosidodecahedron -- Parabola -- Parabolic coordinates -- Parabolic cylinder functions -- Parabolic fractal distribution -- Parabolic subgroup -- Paraboloid -- Paracompact -- Paracompact space -- Paraconsistent analysis -- ...
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List of group theory topics
... subgroups Elementary group theory Identity element Reciprocal Subgroup Coset Transversal Lagrange's theorem Euler's theorem Normal subgroup Hamiltonian group Characteristic subgroup Torsion subgroup Centralizer and normalizer Center of a group ... lemma, Butterfly lemma Schreier refinement theorem Fitting subgroup, generalized Fitting subgroup p-core Group ...
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List of mathematics articles (P)
... truncated dodecahedron -- Parabidiminished rhombicosidodecahedron -- Parabigyrate rhombicosidodecahedron -- Parabola -- Parabolic coordinates -- Parabolic cylinder functions -- Parabolic fractal distribution -- Parabolic subgroup -- Paraboloid -- Paracompact -- Paracompact space -- Paraconsistent analysis -- ...
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