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Element structure of special linear group:SL(2,R)

52 bytes added, 03:22, 22 February 2012
Conjugacy class structure
* Further, the algebraic norm of any nonzero complex number is a ''positive'' real number, and in particular, it is a square. Thus, <math>\R^*/N(\mathbb{C}^*)</math> has size two.
<section begin="summary"/>
{| class="sortable" border="1"
! Nature of conjugacy class !! Eigenvalues !! Characteristic polynomial !! Minimal polynomial !! What set can each conjugacy class be identified with? (rough measure of size of conjugacy class) !! What can the set of conjuacy classes be identified with (rough measure of number of conjugacy classes) !! What can the union of conjugacy classes be identified with? !! Semisimple? !! Diagonalizable over <math>\R</math>? !! Splits in <math>SL_2</math> relative to <math>GL_2</math>?
| Total || NA || NA || NA || NA || ? || ? || ? || ? || ?
|}
<section end="summary"/>
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