Model theoretic interpretation of the octahedron and icosahedron and projective line of F_11.

[gl-yziquel]

Hi.

I noticed your blog post on Kostant's reconstruction of the graph of the truncated icosahedron from the Paley biplane geometry underlying PSL(2,11) and the fixators of automorhisms of the Paley biplane geometry w/r to a point or a line.

I am struggling through it because of the japanese language.

I believe I got that same combinatorial structure but arising from model theory (for the icosahedron and octahedron) and from category theory (with a non-chiral version of Yoneda's lemma giving rise to something aking to the idempotents of the biquaternions, for the Paley biplane geometry). All this arising from the interplay of associativity of 3 elements and of 4 elements.

I would appreciate contacting you (as Kostant is dead...) to see if my combinatorial work may be of interest to you. I have some manuscript documents that may intrigue you.

However, you guard your email address pretty well, and I do not know how to contact you.

Feel free to give me instructions as to how you may be contacted.

Best regards.

Guillaume Yziquel.

[gl-yziquel]

Moreover, your link to Jiro Sekiguchi's discussion of Klein and Poincaré seems to be broken:

https://www2.tsuda.ac.jp/suukeiken/math/suugakushi/sympo14/14_4sekiguchi.pdf

Found on Web Archive: https://web.archive.org/web/20230404150427/https://www2.tsuda.ac.jp/suukeiken/math/suugakushi/sympo14/14_4sekiguchi.pdf

See fix here: #2