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neverendingbooks Posts

neverending.sty

Published June 23, 2005 by lievenlb

You don’t
know how lucky you are to be able to begin a LaTeX-document with
something like \documentclass[a4]{amsart}. This simple line
tells the machine what the size of paper is it has to print to, which
part of that paper has to be filled with text, what the design of
titles, sections etc. is (and probably more). Just convince yourself
(for the sake of argument) that you want to produce a readable
mathematical book on paper of dimensions say 6 by 9 inch. How would you
do this? Simple : all you have to do is to adjust certain TeX-parameters
the way you want! Well, that’s exactly what the _neverendingbooks
design department_ has been doing for the last couple of weeks!

The package we would use was easy enough to find. A long time ago, Geert suggested that we
should use the
memoir package. The fun starts the moment you are foolish enough to
print the manual : 300 pages! After an inspiring account of
book-printing basics over the ages, you are told that you have total
freedom to set your _stock paper size_, how it needs to be
_trimmed_ to get the final result, how you should designs
everything from the title, over abstract, acknowledgement, thanks, table
of contents contents, dedications etc. down to chapter, section and page
styles. In short : ULTIMATE FREEDOM!!!

But, as some of you may
know from experience, there is nothing more frightening to the moderate
autist (and frankly, are there any other mathematicians?) than ultimate
freedom! So, we set up a task-force, had daily brain-storm sessions,
produced numerous trial-prints and eventually came out with something
that came very close to the _better designed book_. Let’s face it
: can you name me _one_ (yeah right, just 1) well-designed
mathematical book? If you don’t believe me, browse through the recent
mathematics-books on amazon (as our design-department
did for a whole week-end, deprived of beverages and other pleasures).
Found anything? Yes?? Please, please let us know! On the other hand, if
you browse through the Art, architecture and
photography section you will spot several extremely good-looking
books very soon. Well, after a week we succeeded in designing the
_arty-farty-fanshi-wanshi_ (as PD1 would name it, jealous that
she was not in on the fun) mathematical book! And, what did we do with
the labours of all this hard work? NOTHING! We simply dropped the whole
idea (if you are a graphics-designer trying to survive within a
mathematics publishing firm (not easy we know, you have all our
sympathy) and want to do something more fun, contact us and if we can
reach an adequate financial agreement we will be happy to send you our
ideas).

So, what went wrong? Nothing really, it just dawned on
us that _NeverEndingBooks.org_ should not go for the
better-designed mathematics book. All our (potential) authors can
publish as easily at Oxford University
Press, the European Mathematical
Society or, if they have no moral objection, at the AMS. So, why
would they choose us instead of these more established publishing
houses? Just because our books look slightly (well let’s face it : a
lot) better? Probably not. We, at neverendingbooks.org should not go for
the better-designed book, we should not go for the book concept at all,
we should invent something entirely NEW & SEXY & USABLE & DESIRING & (I
hope you get the drift!). Next time, I’ll let you in on the first ideas
of our design-department!

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the Klein stack

Published June 15, 2005 by lievenlb

Klein’s
quartic $X$is the smooth plane projective curve defined by
$x^3y+y^3z+z^3x=0$ and is one of the most remarkable mathematical
objects around. For example, it is a Hurwitz curve meaning that the
finite group of symmetries (when the genus is at least two this group
can have at most $84(g-1)$ elements) is as large as possible, which in
the case of the quartic is $168$ and the group itself is the unique
simple group of that order, $G = PSL_2(\mathbb{F}_7)$ also known as
Klein\’s group. John Baez has written a [beautiful page](http://math.ucr.edu/home/baez/klein.html) on the Klein quartic and
its symmetries. Another useful source of information is a paper by Noam
Elkies [The Klein quartic in number theory](www.msri.org/publications/books/Book35/files/elkies.pd).
The quotient map $X \rightarrow X/G \simeq \mathbb{P}^1$ has three
branch points of orders $2,3,7$ in the points on $\mathbb{P}^1$ with
coordinates $1728,0,\infty$. These points correspond to the three
non-free $G$-orbits consisting resp. of $84,56$ and $24$ points.
Now, remove from $X$ a couple of $G$-orbits to obtain an affine open
subset $Y$ such that $G$ acts on its cordinate ring $\mathbb{C}[Y]$ and
form the Klein stack (or hereditary order) $\mathbb{C}[Y] \bigstar G$,
the skew group algebra. In case the open subset $Y$ contains all
non-free orbits, the [one quiver](www.matrix.ua.ac.be/master/coursenotes/onequiver.pdf) of this
qurve has the following shape $\xymatrix{\vtx{} \ar@/^/[dd] \\
\\ \vtx{} \ar@/^/[uu]} $ $\xymatrix{& \vtx{} \ar[ddl] & \\
& & \\ \vtx{} \ar[rr] & & \vtx{} \ar[uul]} $ $\xymatrix{& &
\vtx{} \ar[dll] & & \\ \vtx{} \ar[d] & & & & \vtx{} \ar[ull] \\ \vtx{}
\ar[dr] & & & & \vtx{} \ar[u] \\ & \vtx{} \ar[rr] & & \vtx{} \ar[ur]
&} $ Here, the three components correspond to the three
non-free orbits and the vertices correspond to the isoclasses of simple
$\mathbb{C}[Y] \bigstar G$ of dimension smaller than $168$. There are
two such of dimension $84$, three of dimension $56$ and seven of
dimension $24$ which I gave the non-imaginative names \’twins\’,
\’trinity\’ and \’the dwarfs\’. As we want to spice up later this
Klein stack to a larger group, we need to know the structure of these
exceptional simples as $G$-representations. Surely, someone must have
written a paper on the general problem of finding the $G$-structure of
simples of skew-group algebras $A \bigstar G$, so if you know a
reference please let me know. I used an old paper by Idun Reiten and
Christine Riedtmann to do this case (which is easier as the stabilizer
subgroups are cyclic and hence the induced representations of their
one-dimensionals correspond to the exceptional simples).

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tiger tracks

Published June 13, 2005 by lievenlb

I got
Tracks working under Tiger by trial and error starting with a suggestion
from Jan who found a fix here. From this I stumbled on for an hour or so on my iMac
untill near the very end I found that the tracks-page itself now
has a Tiger-section. So, let’s try to do it all over again from fresh on
my regular machine (a little iBook).

Start with
this page and read it all the way to the comments. There is a
comment by Jamie on installing Rails and MySQL on a fresh Tiger which
looks like the thing I want followed immediately by another post by Jose
Marinez on
Installing Ruby on Rails on Tiger which I decided to follow by the
letter (with one noticeable exception!). So first I downloaded the Rails
installer on Tiger. Next, an install of the Standard version of
MySQL. I used version 4.0 for OS
X 10.3 !!!! NOT 4.1 !!!!. I installed MySQL and the StartUpItem.
Next, I opened Terminal and typed the following commands

– cd
/usr/local/mysql
– sudo chown -R mysql data/
– sudo echo
– sudo ./bin/mysqld_safe &

and verified it by performing a
simple test

/usr/local/mysql/bin/mysql test

Next, I
secured everything by having a root-password

/usr/local/mysql/bin/mysqladmin -u root password
__*

Then I remembered that I’d better
not have to type the whole path so I did a

echo ‘export
PATH=/usr/local/mysql/bin:$PATH’ >> ~/.bash_profile

Also, I want
to admin MySQL via phpmyadmin so I
installed it. Then I enabled my webserver to use PHP using this post though I
did use vi rather than pico! Next, i did a check whether everything
worked fine by typing in safari

http://localhost/~lieven/phpmyadmin/index.php

Followed by
a

sudo gem install mysql –
–with-mysql-dir=/usr/local/mysql

Now, it is time to get the Tracks-package
and to follow these instructions And, it works! Here is the proof :

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