SL2(R)
Sign in to saveAlso known as SL₂(ℝ), SL(2,R), 2×2 real special linear group, SL(2, R)
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\}.
~16 min read
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.
Connections
eigenvectors and eigenvalues
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Lie group
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isometry
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topological group
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orthogonal group
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Möbius transformation
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homography
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upper half-plane
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projective linear group
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matrix group
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Anosov diffeomorphism
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mathematics
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physics
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geometry
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area
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International Standard Book Number
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integer
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real number
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topology
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digital object identifier
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