SL2(R)
Sign in to saveIn mathematics, the special linear group SL(2, R) or SL2(R) is the group of 2 × 2 real matrices with determinant one: \mbox{SL}(2,\mathbf{R}) = \left\{ \begin{pmatrix} a & b \\ c & d \end{pmatrix} \colon a,b,c,d \in \mathbf{R}\mbox{ and }ad-bc=1\right\}.
Article
15 sectionsContents
- Descriptions
- Homographies
- Möbius transformations
- Adjoint representation
- Classification of elements
- Elliptic elements
- Parabolic elements
- Hyperbolic elements
- Conjugacy classes
- Iwasawa or KAN decomposition
- Topology and universal cover
- Algebraic structure
- Representation theory
- See also
- References
In mathematics, the special linear group SL(2, R) or SL2(R) is the group of 2 × 2 real matrices with determinant one: \mbox{SL}(2,\mathbf{R}) = \left\{ \begin{pmatrix} a & b \\ c & d \end{pmatrix} \colon a,b,c,d \in \mathbf{R}\mbox{ and }ad-bc=1\right\}.
It is a connected non-compact simple real Lie group of dimension 3 with applications in geometry, topology, representation theory, and physics.