Lorentz group - Wikipedia--> special attention to Robin Chapman

From: Roger Bagula (tftn_at_earthlink.net)
Date: 07/10/04 

Date: Sat, 10 Jul 2004 23:44:16 GMT

    The covering spin group

Like the rotation group SO(3), the restricted Lorentz group is not
simply connected; rather, it is doubly connected. That is, the
fundamental group <http://en.wikipedia.org/wiki/Fundamental_group> of
SO+(1, 3) is isomorphic <http://en.wikipedia.org/wiki/Isomorphic> to Z2
<http://en.wikipedia.org/wiki/Cyclic_group>.

The universal cover <http://en.wikipedia.org/wiki/Universal_cover> of
the restricted Lorentz group can be identified with the special linear
group <http://en.wikipedia.org/wiki/Special_linear_group> SL(2, C). The
restricted Lorentz group is isomorphic to the quotient group
<http://en.wikipedia.org/wiki/Quotient_group> SL(2, C)/{±1} also known
as the projective linear group
<http://en.wikipedia.org/wiki/Projective_linear_group>, PSL(2, C). This
group shows up in another guise as the group of all Möbius
transformations <http://en.wikipedia.org/wiki/M%F6bius_transformation>
of the Riemann sphere <http://en.wikipedia.org/wiki/Riemann_sphere>.

In applications to quantum mechanics
<http://en.wikipedia.org/wiki/Quantum_mechanics> the group SL(2, C) is
sometimes called the Lorentz group.

http://en.wikipedia.org/wiki/Lorentz_group 

-- 
Respectfully, Roger L. Bagula
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