Starting with Sl 2 (r) Group
نویسنده
چکیده
The simplest objects with non-commutative multiplication are 2×2 matrices with real entries. Such matrices of determinant one form a closed set under multiplication (since det(AB) = detA · detB), the identity matrix is among them and any such matrix has an inverse (since detA 6= 0). In other words those matrices form a group, the SL2(R) group [7]—one of the two most important Lie groups in analysis. Another group is the Heisenberg group [2] and their nearest contestant the “ax+ b”-group is only a subgroup of SL2(R), see the nominator in (1). The simplest non-linear transforms of the real line—linear-fractional or Möbius map—may also be associated with 2× 2 matrices: (1)
منابع مشابه
An SL(2, Z) Multiplet of Type IIB Super Five-Branes
It is well-known that the low energy string theory admits a non-singular solitonic super five-brane solution which is the magnetic dual to the fundamental string solution. By using the symmetry of the type IIB string theory, we construct an SL(2, Z) multiplet of magnetically charged super five-branes starting from this solitonic solution. These solutions are characterized by two integral three-...
متن کاملQuantum Parafermions in the SL(2, R)/U(1) WZNW Black Hole Model
Starting with its classical parafermion algebra, we consider the quantisation of the SL(2, R)/U(1) WZNW black hole model.
متن کاملDynamics of the Mapping Class Group on the Moduli of a Punctured Sphere with Rational Holonomy
Let M be a four-holed sphere and Γ the mapping class group of M fixing the boundary ∂M . The group Γ acts on MB(SL(2,C)) = Hom+B (π1(M), SL(2,C))/ SL(2,C) which is the space of completely reducible SL(2,C)-gauge equivalence classes of flat SL(2,C)-connections on M with fixed holonomy B on ∂M . Let B ∈ (−2, 2) and MB be the compact component of the real points of MB(SL(2,C)). These points corres...
متن کاملSL(2, Z) Multiplets of Type II Superstrings in D < 10
It has been shown recently that the toroidally compactified type IIB string effective action possesses an SL(2, R) invariance. Using this symmetry we construct an infinite family of macroscopic string-like solutions permuted by SL(2, Z) group for type II superstrings in 4 ≤ D < 10. These solutions, which formally look very similar to the corresponding solutions in D = 10, are characterized by t...
متن کاملFundamental domains for SL 2 ( Z ) and Γ θ
1. H as homogeneous space for G = SL 2 (R) 2. Fundamental domain for Γ = SL 2 (Z) on H 3. Inversion and translation generate SL 2 (Z). 4. Re-enabling the action of SL 2 (R) 5. Fundamental domain for Γ θ and Γ(2) 6. Generators for Γ θ 7. Theta series are modular forms The real line R, being a group, is a homogeneous space in the sense that (of course) it acts transitively on itself. The upper ha...
متن کامل