Thank you! Just very recently, Georgia Benkart and Tom Halverson got a step further: https://arxiv.org/abs/1707.01410

I am still trying to figure out a refinement, I hope I’ll manage!

]]>Nice! I hadn’t known, or had forgotten, that you are collaborating with Bruce Westbury. I really like his paper on a diagrammatic approach to normed division algebras (or more precisely, composition algebras).

]]>Indeed, the idea of Blake Stacey is what Bruce and I try to expand upon in https://arxiv.org/abs/1408.3592 – warning: this paper is still work in progress…

(thank you for fixing my syntax!)

]]>Hey, that’s cool! I hadn’t thought of linearizing this category! This is connected to Blake Stacey’s comment on taking formal linear combinations of morphisms in a category to get a new ‘linear’ category. It’s nice how the representation theory of the symmetric group shows up here. This could be pretty important, at least in applications of network theory to *linear* systems.

By the way, to use TeX here, you have to enclose the math with

$latex $

with the word ‘latex’ appearing directly after the first dollar sign, no space between, but then a space after it.

]]>More precisely, when you compose two morphisms, some blocks may lose contact to the input and the output. In this case, these blocks (let’s say there are of them) are omitted and the result is multiplied with the -th power of a parameter, usually denoted .

When is small, there is a basis of the centralizer algebra indexed (!) by set partitions into at most blocks.

Still, there are some mysterious open questions…

]]>Davis’s law of small devices:

A device can be made arbitrarily small if it doesn’t have to work.