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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeOct 10th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded statement of and references for some of the homotopy groups of $E_8$ to [[E8]]

   added statement of and references for some of the homotopy groups of $E_8$ to E8

2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeMar 16th 2018
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexCurious that the extra information on [[E8]] focuses on its homotopy groups, for [[E7]] it's its two smallest representations, and for [[E6]] it's the relationship of a split form with $SL(3, \mathbb{O})$. Is there no such interesting decomposition of the 248-dim adjoint rep of $E_8$ as the decomposition of the 56-dim of $E_7$?

   Curious that the extra information on E8 focuses on its homotopy groups, for E7 it’s its two smallest representations, and for E6 it’s the relationship of a split form with $SL(3, \mathbb{O})$.

   Is there no such interesting decomposition of the 248-dim adjoint rep of $E_8$ as the decomposition of the 56-dim of $E_7$?

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMar 16th 2018
   • (edited Mar 16th 2018)
   • PermaLink
   Author: Urs
   Format: MarkdownItex"Focus" is a big word for what is a sporadic jotting down of random facts that I happened to feel like making a stubby note of. Some day somebody should invest some energy into these entries. Until then their choice of information is not taken to be an indication of its relevance.

   “Focus” is a big word for what is a sporadic jotting down of random facts that I happened to feel like making a stubby note of. Some day somebody should invest some energy into these entries. Until then their choice of information is not taken to be an indication of its relevance.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeMay 8th 2019
   • (edited May 8th 2019)
   • PermaLink
   Author: Urs
   Format: MarkdownItexstarted a Properties section "Subgroups" ([here](https://ncatlab.org/nlab/show/E8#Subgroups)), but so far just with a quick pointer to _[[SemiSpin(16)]]_ <a href="https://ncatlab.org/nlab/revision/diff/E8/12">diff</a>, <a href="https://ncatlab.org/nlab/revision/E8/12">v12</a>, <a href="https://ncatlab.org/nlab/show/E8">current</a>

   started a Properties section “Subgroups” (here), but so far just with a quick pointer to SemiSpin(16)

   diff, v12, current

5. • CommentRowNumber5.
   • CommentAuthorSamuel Adrian Antz
   • CommentTimeJul 17th 2024
   • PermaLink
   Author: Samuel Adrian Antz
   Format: MarkdownItexUsed unicode subscripts for indices of [[exceptional Lie groups]] including title and links. When not linked, usual formulas are used. See discussion [here](https://nforum.ncatlab.org/discussion/18215/title-convention). Links will be re-checked after all titles are changed. (Removed two redirects for "E8" from the top and added one for "E8" at the bottom of the page.) <a href="https://ncatlab.org/nlab/revision/diff/E%E2%82%88/15">diff</a>, <a href="https://ncatlab.org/nlab/revision/E%E2%82%88/15">v15</a>, <a href="https://ncatlab.org/nlab/show/E%E2%82%88">current</a>

   Used unicode subscripts for indices of exceptional Lie groups including title and links. When not linked, usual formulas are used. See discussion here. Links will be re-checked after all titles are changed. (Removed two redirects for “E8” from the top and added one for “E8” at the bottom of the page.)

   diff, v15, current