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2. SL2 (R) - Wikipedia

   en.wikipedia.org/wiki/SL2(R)

   The finite-dimensional representation theory of SL(2, R) is equivalent to the representation theory of SU(2), which is the compact real form of SL(2, C). In particular, SL(2, R) has no nontrivial finite-dimensional unitary representations. This is a feature of every connected simple non-compact Lie group.

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4. Representation theory of SL2(R) - Wikipedia

   en.wikipedia.org/.../Representation_theory_of_SL2(R)

   It generates the center of the universal enveloping algebra of the complexified Lie algebra of SL(2, R). The Casimir element acts on any irreducible representation as multiplication by some complex scalar μ 2. Thus in the case of the Lie algebra sl 2, the infinitesimal character of an irreducible representation is specified by one complex number.

5. Special linear group - Wikipedia

   en.wikipedia.org/wiki/Special_linear_group

   These elements are "special" in that they form an algebraic subvariety of the general linear group – they satisfy a polynomial equation (since the determinant is polynomial in the entries). When R is the finite field of order q, the notation SL(n, q) is sometimes used.

6. Special linear Lie algebra - Wikipedia

   en.wikipedia.org/wiki/Special_linear_Lie_algebra

   The algebra plays an important role in the study of chaos and fractals, as it generates the Möbius group SL(2,R), which describes the automorphisms of the hyperbolic plane, the simplest Riemann surface of negative curvature; by contrast, SL(2,C) describes the automorphisms of the hyperbolic 3-dimensional ball.

7. sl2-triple - Wikipedia

   en.wikipedia.org/wiki/Sl2-triple

   of the Lie algebra sl 2 of 2 by 2 matrices with zero trace. It follows that sl 2-triples in g are in a bijective correspondence with the Lie algebra homomorphisms from sl 2 into g. The alternative notation for the elements of an sl 2-triple is {H, X, Y}, with H corresponding to h, X corresponding to e, and Y corresponding to f. H is called a ...

8. Table of Lie groups - Wikipedia

   en.wikipedia.org/wiki/Table_of_Lie_groups

   SL(1,R) is a single point and therefore compact and simply connected sl(n,R) n 2 −1 SL(2,R) Orientation-preserving isometries of the Poincaré half-plane, isomorphic to SU(1,1), isomorphic to Sp(2,R). N 0 Z: The universal cover has no finite-dimensional faithful representations. sl(2,R) 3 O(n) orthogonal group: real orthogonal matrices: Y Z 2 –

9. Cialis Side Effects: What to Expect (& How to Avoid Them) - AOL

   www.aol.com/cialis-side-effects-expect-avoid...

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