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Tag: noncommutative

hectic days

Hectic
days ahead! Today, there is the Ph.D. defense of Stijn Symens and the
following two days there is a meeting in Ghent where Jacques
Alev and me organize a special session on non-commutative algebra. Here
is the programme of that section

Session 1 (Friday 20 May)
— chair : Jacques Alev (Univ. Reims)

15.30-16.25 : Iain Gordon (Glasgow, United
Kingdom) : “Rational Cherednik algebras and resolutions of
symplectic
singularities”

16.25-16.35 : break

16.35-17.30 : Olivier Schiffmann (ENS Paris, France) :
“Elliptic Hall algebras and spherical Cherednik algebras”

Session 2 (Saturday 21 May) — chair : Lieven Le Bruyn
(Univ. Antwerp)

14.30-15.15 : Markus
Reineke
(Munster, Germany) : “Geometry of Quiver Moduli”

15.15-16.00 : Raf Bocklandt &
Geert Van de Weyer
(Antwerp, Belgium) : “The power of slicing in noncommutative
geometry”

Afterwards it will be time to take a short
vacation (and do some cycling in the French mountains). Here is my
reading list for next week :

The dark Eye – Ingrid
Black
: Simply because I read her previous novel The dead

Brass – Helen Walsh : I
read the first 3 or 4 pages in the shop and couldn\’t stop …

Fleshmarked Alley – Ian
Rankin
: Hey, it\’s vacation!

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markdown2use

Here some
possible uses of Markdown and the
HumaneText Service.
As an example, let us take the
noncommutative geometry & algebra page
maintained by Paul Smith.

If you copy the source of this page to BBEdit and use the
html2txt.py script in the #! menu (see
this post)
you get a nicely readable Markdown-file which strips the page of all its
layout and which is easy to modify, for example to include author and
URL at the start, remove some additional empty lines, make relative URLs
absolute and so on.

Applying the Markdown.pl
script to it one gets a nice RetroCool version
of the page. For starters, this gives a way to make your own collection
of websites you like in a uniform layout (of course, later on you can
add your own CSS to them).

More important is that the
Markdown-version (see here for
the text-file) is extremely readable and allows to _mine_ all
links easily (as you can see all links contained in the HTML-page are
referenced together at the end of the file). So, this is a quick way to
collect homepage- and email-links from link-pages.

Btw. there
are different ways to include links in a markdown text, for example I
like to write it immediately after the reference, so doing a Markdown.pl
followed by a html2txt.py doesn’t have to reproduce your original file
and fortunately you will always end up with a file having all links
referenced at the end. So, this procedure allows you to have uniformity
in a collection of markdown-files.

Equally important for me (for
later use in an intelligent database using DevonThink ) is that the Markdown file is the best way to safe the
HTML file in the database (as a RTF file) while maintaining readability
(which is important when DevonThink returns snippets of
information).

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B for bricks

Last time we
argued that a noncommutative variety might be an _aggregate_
which locally is of the form $\mathbf{rep}~A$ for some affine (possibly
non-commutative) $C$-algebra $A$. However, we didn't specify what we
meant by 'locally' as we didn't define a topology on
$\mathbf{rep}~A$, let alone on an arbitrary aggregate. Today we will start
the construction of a truly _non-commutative topology_ on
$\mathbf{rep}~A$.
Here is the basic idea : we start with a thick
subset of finite dimensional representations on which we have a natural
(ordinary) topology and then we extend this to a non-commutativce
topology on the whole of $\mathbf{rep}~A$ using extensions. The impatient
can have a look at my old note A noncommutative
topology on rep A
but note that we will modify the construction here
in two essential ways.
In that note we took $\mathbf{simp}~A$, the
set of all fnite dimensional simple representations, as thick subset
equipped with the induced Zariski topology on the prime spectrum
$\mathbf{spec}~A$. However, this topology doesn't behave well with
respect to the gluings we have in mind so we will extend $\mathbf{simp}~A$
substantially.

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