Tomorrow
I’ll start with the course Projects in non-commutative geometry
in our masterclass. The idea of this course (and its companion
Projects in non-commutative algebra run by Fred Van Oystaeyen) is
that students should make a small (original if possible) work, that may
eventually lead to a publication.
At this moment the students
have seen the following : definition and examples of quasi-free algebras
(aka formally smooth algebras, non-commutative curves), their
representation varieties, their connected component semigroup and the
Euler-form on it. Last week, Markus Reineke used all this in his mini-course
Rational points of varieties associated to quasi-free
algebras. In it, Markus gave a method to compute (at least in
principle) the number of points of the non-commutative Hilbert
scheme and the varieties of simple representations over a
finite field. Here, in principle means that Markus demands a lot of
knowledge in advance : the number of points of all connected components
of all representation schemes of the algebra as well as of its scalar
extensions over finite field extensions, together with the action of the
Galois group on them … Sadly, I do not know too many examples were all
this information is known (apart from path algebras of quivers).
Therefore, it seems like a good idea to run through Markus’
calculations in some specific examples were I think one can get all this
: free products of semi-simple algebras. The motivating examples
being the groupalgebra of the (projective) modular group
PSL(2,Z) = Z(2) * Z(3) and the free matrix-products $M(n,F_q) *
M(m,F_q)$. I will explain how one begins to compute things in these
examples and will also explain how to get the One
quiver to rule them all in these cases. It would be interesting to
compare the calculations we will find with those corresponding to the
path algebra of this one quiver.
As Markus set the good
example of writing out his notes and posting them, I will try to do the
same for my previous two sessions on quasi-free algebras over the next
couple of weeks.
neverendingbooks Posts
I
bought a couple of X10-building blocks : a tranceiver, an appliance- and
a lamp-module, a computer-interface and a motion detector and started
playing using the Indigo help-page. All modules worked immediately
and getting them under Indigo‘s control was also no problem.
Clearly it is fun to control a living room lamp and the coffee maker
from your computer but it gets even better when you program actions.
With Indigo you can let your home automation system react to
incoming emails. For example, if it is a rainy workday and I want to
have a cup of coffee when I bicycle home I can just send an email with
subject “Make coffee”. Indigo checks at home my email every
two-minutes and when it scans this subject-title it will send a signal
to the coffee maker to turn on (assuming I filled it with water and
coffee beforehand, otherwise it may result in a fire…). One can also
program it the other direction. For example, with Indigo I can
program things so that when the motion detector detects movement from
opening the front door, I can ask to send an email to work (or to a
mobile but as I am not using these things this is no option) with
message “Someone just walked in…”.
Getting the
motion-detector (MS13 for the experts) working was so far the second
hardest thing to do. I couldnt work out how to give it a home&unit
code but I found a readable manual page which made everything work. I have to
remember to change the other default options of the detector.
The hardest thing to solve was to get the Indigo Web Interface working. Following the
instructions on this page to the letter I thought that I could control
my X10-stuff from any other computer (assuming Indigo is running
on my iBook) by accessing the
URL
http://iBookLieven.local/cgi-bin/Indigo.acgi
but all I got
was a ‘Server Error’. I figured out that the mistake was caused by the
acgi
dispatcher program. The first time this is run, it asks for your
admin password to write some extra lines to the httpd.conf
Apache configuration file, but for some strange reason it didn’t want
to accept my password… Changing permissions on httpd.conf and
even creating a genuine root-account didn’t help so I was stuck
for a while. But then I found the Mac OS X
hack #91 which not only explains the use of the dispatcher tool but
also explains what it adds to the httpd.conf-file. So, I just
copied the following lines manually at the end of
httpd.conf
#BEGIN acgi dispatcher Include /Library/WebServer/CGI-Executables/dispatcher.app/Contents/acgi.conf\r\ nEND acgi dispatcher
did restart the Apache webserved by a
sudo apachectl graceful
after which the acgi dispatcher
tool started up without problems and I got a working Indigo Web
Interface. I must remember to put both Indigo and the
dispatcher into my StartUp items.
The Web Interface is
very basic compared to other house automation programs such as MisterHouse
which makes up for its sexist name by being open source! It is entirely
written in Perl
but as I am only halfway through the Learning Perl book at the moment, this will have
to wait a bit longer…
I\’ve barely managed to implement the six
great tips for homemade dot mac servers by Alan
Graham or he is already off on a new project : Home Automation
with Mac OS X. I thought that home automation only could be
installed in new, highly wired, houses but I was wrong. In part
1 Alan Graham gives an overview why you might consider home
automation, gives the set-up in his house and outlines the hardware
necessary to do it. Clearly, most of his hardware is American but even
in Belgium it is not difficult to find vendors, for example intellihome.be. One can either control the
X10-machinery by remote control or via computer. For Macintosh Alan
Graham suggests to use the indigo program, of which one can download a fully
functional version for a 30 day tryout. The only piece I could not find
(yet) in Belgium was the PowerLink USB device but there is a serial-port
alternative available which seems to work just fine using a USB to
Serial cable (which are fairly expensive). In part 2 Alan Graham explains the basics of X10 technology and how you can
install all the hardware. In part 3 and later he promises to explain the
software part of things (if he hasnt started a new project by
then…).