[seqfan] Re: Spinors and Bott periodicity

[Andrew Weimholt]

I also attempted to research this topic and based on various papers and
articles I found, I agree that A034583 and A034584 are correct.

However, even though spinors are closely related to Clifford Algebras, they
are not synonymous, so
if Baez is correct, then we have a new sequence.

After quite a bit of searching, the best reference I was able to find on
dimensions of spinors in n-dimensional space was the Wikipedia page on
spinors. http://en.wikipedia.org/wiki/Spinor - see the section "summary in
low-dimensions" at the bottom.
If I'm reading it right, then the sequence begins 1, 2, 4, 4, 4, 4, 8, 8,
... in agreement with the table in Baez's video, and thereafter, a(n+8) =
16*a(n) due to Bott Periodicity (which is also the principle behind the
same relation in A034583 and A034584).

Andrew


On Wed, Jan 29, 2014 at 7:58 PM, William Keith <william.keith at gmail.com>wrote:

> Bear in mind that I know almost nothing about spinors.  My only source is
> the video and a poke at Wikipedia, and so I am not at all sure of the
> proposed title for the new sequence.  I doubt that spinors are "in" real
> space.  Perhaps "the dimension of the space of spinors acted on by the
> double cover of n-dimensional real vector space"?  Although I'm not 100%
> certain of that either.
>
> The sequence is simple enough to define.  It's just that I'm not sure what
> he's describing.  Sorry.
>
> William
>
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