John Baez "This Week's Finds in Mathematical Physics"

[Martin]

http://math.ucr.edu/home/baez/week212.html

 

a new issue of "TWF" came out today

 

it seems there are only 4 possible "normed division algebras" in Baez terminology

and they are the reals, the complexnumbers, the quaternions, and the octonions

 

and it turns out that by introducing a kind of Z₂ symmetry

or a very simple kind of twopart boolean symmetry you can EXTEND this

and get more nice number systems which are analogs of the

"normed division algebras"

 

I am not sure i have the terminology right, but it belongs in mdrn algebra and also in physics because these new systems are called superalgebras, or else

"super division algebras"

and they are like the other 4 except they have "supersymmetry".

just looked at the new TWF and ....well I just glanced at it....cant say more

[Dave]

I absolutely love this:

 

Mathematicians should have gotten this idea and run with it first, but physicists did - and maybe it's turned them into mathematicians.

 

[matt grime]

The thing is, mathematicians have very little interest in the Z_2 grading, at least with that phrasing, in and of themselves anymore than any other grading. Whereas mathematical physicists find these specifically coming up all the time, so I find that quote disingenuous, but then I'm reading out of context, and Jon often has his tongue in his cheek when writing such things.

[matt grime]

Right, scanned through it now. Odd that two of the big names in it are Karoubi and Deligne, who might recognize being called physicists.

 

Topologists, and homomlogical algebraists, if they're different, have had such things as Z_2 graded objects for ages. We just never call them super. Damn physicists stealing our ideas.... (note there is _humour_ in this post)