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From: scott%tekcrl.labs.tek.com@RELAY.CS.NET
Newsgroups: bit.listserv.frac-l
Subject: Re: Brooks/Matelski & Mandelbrot
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Date: 9 Feb 90 00:05:21 GMT
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In-Reply-To:  Your message of Thu, 08 Feb 90 15:36:47 -0500.

> what is does the acronym PSL stand for?

It stands for "projective special linear".

The "special linear" group SL(2,C) consists of 2x2 matrices with complex
entries whose determinant is 1.  GL(2,C) ("general linear") is the group
of 2x2 nonsingular complex matrices.

The projective groups are certain subgroups of the linear groups whose
elements are equivalence classes of matrices.  An element of PGL(2,C)
is a set of matrices {M*c1 : for M in GL(2,C), c in C, and 1 the identity
matrix}.  An element of PSL(2,C) is a set of matrices
{M*s1 : for M in SL(2,C) and s in C with s*s = 1}.

PSL(2,C) is (I believe) a "simple" group, meaning it can't be decomposed
into smaller groups in certain ways.  Simple groups are analogous to prime
numbers, in that they're the basic building blocks for constructing other
groups.

For more info, check books on algebra and group theory.

-- Scott Huddleston