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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMay 15th 2019
   • PermaLink
   Author: Urs
   Format: MarkdownItexPage created, but author did not leave any comments. <a href="https://ncatlab.org/nlab/revision/exceptional+structures/1">v1</a>, <a href="https://ncatlab.org/nlab/show/exceptional+structures">current</a>

   Page created, but author did not leave any comments.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMay 15th 2019
   • PermaLink
   Author: Urs
   Format: MarkdownItexmade page name singular <a href="https://ncatlab.org/nlab/revision/exceptional+structure/1">v1</a>, <a href="https://ncatlab.org/nlab/show/exceptional+structure">current</a>

   made page name singular

   v1, current

3. • CommentRowNumber3.
   • CommentAuthorDavid_Corfield
   • CommentTimeMay 15th 2019
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexAdded some more cases, and pointed out some interrelations. <a href="https://ncatlab.org/nlab/revision/diff/exceptional+structure/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/exceptional+structure/2">v2</a>, <a href="https://ncatlab.org/nlab/show/exceptional+structure">current</a>

   Added some more cases, and pointed out some interrelations.

   diff, v2, current

4. • CommentRowNumber4.
   • CommentAuthorDavid_Corfield
   • CommentTimeMay 15th 2019
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexAdded a reference * Yang-Hui He, [[John McKay]], _Sporadic and Exceptional_, ([arXiv:1505.06742](https://arxiv.org/abs/1505.06742)) <a href="https://ncatlab.org/nlab/revision/diff/exceptional+structure/5">diff</a>, <a href="https://ncatlab.org/nlab/revision/exceptional+structure/5">v5</a>, <a href="https://ncatlab.org/nlab/show/exceptional+structure">current</a>

   Added a reference

   • Yang-Hui He, John McKay, Sporadic and Exceptional, (arXiv:1505.06742)

   diff, v5, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeMay 15th 2019
   • PermaLink
   Author: Urs
   Format: MarkdownItexthanks, hadn't seen that (and it seems unpublished?) BTW, we do have an entry for [[Yang-Hui He]] <a href="https://ncatlab.org/nlab/revision/diff/exceptional+structure/6">diff</a>, <a href="https://ncatlab.org/nlab/revision/exceptional+structure/6">v6</a>, <a href="https://ncatlab.org/nlab/show/exceptional+structure">current</a>

   thanks, hadn’t seen that (and it seems unpublished?) BTW, we do have an entry for Yang-Hui He

   diff, v6, current

6. • CommentRowNumber6.
   • CommentAuthorDavid_Corfield
   • CommentTimeMay 17th 2019
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexAdded connection and reference between the Leech lattice and the octonions. <a href="https://ncatlab.org/nlab/revision/diff/exceptional+structure/7">diff</a>, <a href="https://ncatlab.org/nlab/revision/exceptional+structure/7">v7</a>, <a href="https://ncatlab.org/nlab/show/exceptional+structure">current</a>

   Added connection and reference between the Leech lattice and the octonions.

   diff, v7, current

7. • CommentRowNumber7.
   • CommentAuthorDavid_Corfield
   • CommentTimeMay 17th 2019
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexI added a link to an associated talk by Wilson. He ends with applications: >* Perhaps this gives us a better understanding of why the Leech lattice exists. >* Perhaps it will give us new ways to prove important properties of the Leech lattice and the Conway group. >* Perhaps we can use octonions to simplify the construction of the Monster. >* Perhaps it will explain the ‘2-local group’ BDI(4) which contains Co3 and looks as though it should be some kind of twist of ‘skew-symmetric 3×3 matrices over octonions’ Could one dare to hope that [growing the superpoint](https://nforum.ncatlab.org/discussion/6701/universal-exceptionalism/?Focus=60902#Comment_60902) $\mathbb{R}^{0|3}$ could make contact with these things?

   I added a link to an associated talk by Wilson.

   He ends with applications:

   • Perhaps this gives us a better understanding of why the Leech lattice exists.

   • Perhaps it will give us new ways to prove important properties of the Leech lattice and the Conway group.

   • Perhaps we can use octonions to simplify the construction of the Monster.

   • Perhaps it will explain the ‘2-local group’ BDI(4) which contains Co3 and looks as though it should be some kind of twist of ‘skew-symmetric 3×3 matrices over octonions’

   Could one dare to hope that growing the superpoint $\mathbb{R}^{0|3}$ could make contact with these things?

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeJun 27th 2019
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to * Piero Truini, Michael Rios, Alessio Marrani, _The Magic Star of Exceptional Periodicity_ ([arXiv:1711.07881](https://arxiv.org/abs/1711.07881)) prodded by today's * Michael Rios, Alessio Marrani, David Chester, _Exceptional Super Yang-Mills in $D=27+3$ and Worldvolume M-Theory_ ([arXiv:1906.10709](https://arxiv.org/abs/1906.10709)) Haven't absorbed either yet. But if these hold water, I should. <a href="https://ncatlab.org/nlab/revision/diff/exceptional+structure/9">diff</a>, <a href="https://ncatlab.org/nlab/revision/exceptional+structure/9">v9</a>, <a href="https://ncatlab.org/nlab/show/exceptional+structure">current</a>

   added pointer to

   • Piero Truini, Michael Rios, Alessio Marrani, The Magic Star of Exceptional Periodicity (arXiv:1711.07881)

   prodded by today’s

   • Michael Rios, Alessio Marrani, David Chester, Exceptional Super Yang-Mills in $D=27+3$ and Worldvolume M-Theory (arXiv:1906.10709)

   Haven’t absorbed either yet. But if these hold water, I should.

   diff, v9, current

9. • CommentRowNumber9.
   • CommentAuthorUrs
   • CommentTimeJan 16th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded publication data for this item: * [[Piero Truini]], [[Michael Rios]], [[Alessio Marrani]], *The Magic Star of Exceptional Periodicity*, J. Phys.: Conf. Ser. **1194** (2019) 012106 &lbrack;[arXiv:1711.07881](https://arxiv.org/abs/1711.07881), [doi:10.1088/1742-6596/1194/1/012106](https://iopscience.iop.org/article/10.1088/1742-6596/1194/1/012106)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/exceptional+structure/11">diff</a>, <a href="https://ncatlab.org/nlab/revision/exceptional+structure/11">v11</a>, <a href="https://ncatlab.org/nlab/show/exceptional+structure">current</a>

   added publication data for this item:

   • Piero Truini, Michael Rios, Alessio Marrani, The Magic Star of Exceptional Periodicity, J. Phys.: Conf. Ser. 1194 (2019) 012106 [arXiv:1711.07881, doi:10.1088/1742-6596/1194/1/012106]

   diff, v11, current