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October 2, 2009

Special Issue on “Categorification in Representation Theory”

Posted by Alexander Hoffnung

Aaron Lauda, Anthony Licata and Alistair Savage (all of whom we are lucky to have speaking at the AMS meeting at Riverside this Fall) have just announced their Special Issue on “Categorification in Representation Theory” of the International Journal of Mathematics and Mathematical Statistics.

The official Call for Papers is here.

The topics to be considered are:

*Geometric categorifications, including geometric realizations of crystals, representations of quantum groups, braid group actions, and derived equivalences

*Combinatorial categorifications of quantum groups, Hecke algebras, cluster algebras, and relations between combinatorial constructions and geometric categorifications

*Diagrammatic categorifications, especially diagrammatic interpretations of geometric categorifications

*Categorified link invariants with representation theoretic origins

I am sure there are plenty of people floating around here with nice articles to submit.

Posted at October 2, 2009 6:33 PM UTC

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Re: Special Issue on “Categorification in Representation Theory”

In case some of you didn’t notice: Alex Hoffnung is now an official host at the nn-Café, and this is his first post in that capacity — as opposed to a “guest post”.

Hip, hip, hoorah!

Posted by: John Baez on October 2, 2009 8:09 PM | Permalink | Reply to this

Re: Special Issue on “Categorification in Representation Theory”

Wow; the list of hosts is a lot longer than the last time I noticed it. When did that happen?

Posted by: Tim Silverman on October 2, 2009 8:49 PM | Permalink | Reply to this

Re: Special Issue on “Categorification in Representation Theory”

We sneaked (the wise old internet tells me “snuck” is not traditionally an English word) in the back door rather recently.

Posted by: Alex Hoffnung on October 3, 2009 2:07 AM | Permalink | Reply to this

Re: Snuck

“Internet” and “blog” are also not traditionally English words, but they’re both in common usage. “Snuck” is a great word and you’ll find in work by Kerouac and Chandler, so I think it’s perfectly acceptable. And it just sounds great, especially with a solid northern English vowel in the middle – it almost sounds as good as “snog”.

Posted by: Simon Willerton on October 3, 2009 12:07 PM | Permalink | PGP Sig | Reply to this

Re: Special Issue on “Categorification in Representation Theory”

David, Urs and I decided to increase the number of nn-Café hosts a while back. This won’t make much difference until the new guys start posting articles. I suspect they’ll never post as much as the original hosts. But that’s fine.

Posted by: John Baez on October 4, 2009 12:52 AM | Permalink | Reply to this

Re: Special Issue on “Categorification in Representation Theory”

this is his first post in that capacity

His post page says that he made one over a month ago.

Posted by: Toby Bartels on October 4, 2009 12:59 AM | Permalink | Reply to this

Re: Special Issue on “Categorification in Representation Theory”

Whoops, you’re right. I helped him post that — he was just learning how the nn-Café works.

Anyway, this is his first post where I fired up my web browser in the morning and said “Surprise! A post by Alex!” And that’s a good feeling.

Posted by: John Baez on October 4, 2009 4:34 PM | Permalink | Reply to this

Generalized Burnside Theorem; Re: Special Issue on “Categorification in Representation Theory”

Is this the right thread for me to ask how this connects to n-Categorified QM? It looked good to me at first pass, because of its foundationally solid “construction of the algebra of observables.” But I was lost when I took Module Theory at Caltech, and never got far enough in Category Theory to be dangerous in grad school.

Title: The Generalized Burnside Theorem in noncommutative deformation theory
Authors: Eivind Eriksen
Comments: AMS-LaTeX, 7 pages
Subjects: Algebraic Geometry(math.AG); Rings and Algebras
(math.RA); Representation Theory (math.RT)

Let A be an associative algebra over a field, and let M be a finite family of right A-modules. Study of the noncommutative deformation functor of the family M leads to the construction of the algebra of observables and the Generalized Burnside Theorem, due to Laudal. In this paper, we give an overview of aspects of noncommutative deformations closely connected to the Generalized Burnside Theorem.

Posted by: Jonathan Vos Post on October 5, 2009 8:05 PM | Permalink | Reply to this

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