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1. • CommentRowNumber1.
   • CommentAuthorDavidRoberts
   • CommentTimeAug 14th 2013
   • (edited Aug 14th 2013)
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexI created a small page for [[compact symplectic group]], which is not the same as the [[symplectic group]], and added some sentences at both to disambiguate. I'm also working on an entry [[orthogonal group of an inner product space]], which will give the general treatment that covers $O(n)$, $U(n)$ and $Sp(n)$ (and other cases of mixed signature, like $O(n,m)$). There are interesting charts for $O(n,\mathbb{K})$ using its Lie algebra (in fact various tangent spaces) which don't come from the exponential mapping, and my aim is to get a reasonably full treatment of these in there.

   I created a small page for compact symplectic group, which is not the same as the symplectic group, and added some sentences at both to disambiguate. I’m also working on an entry orthogonal group of an inner product space, which will give the general treatment that covers $O(n)$, $U(n)$ and $Sp(n)$ (and other cases of mixed signature, like $O(n,m)$).

   There are interesting charts for $O(n,\mathbb{K})$ using its Lie algebra (in fact various tangent spaces) which don’t come from the exponential mapping, and my aim is to get a reasonably full treatment of these in there.

2. • CommentRowNumber2.
   • CommentAuthorDavidRoberts
   • CommentTimeAug 14th 2013
   • (edited Aug 14th 2013)
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexClearly we get a real manifold when $\mathbb{K}$ is a associative division algebra over $\mathbb{R}$, but what about *-algebras over other complete fields? Just wondering.

   Clearly we get a real manifold when $\mathbb{K}$ is a associative division algebra over $\mathbb{R}$, but what about *-algebras over other complete fields? Just wondering.

3. • CommentRowNumber3.
   • CommentAuthorTobyBartels
   • CommentTimeAug 26th 2013
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexI added another characterization of $Sp(n)$. I would be inclined to put all of the material at [[orthogonal group of an inner product space]] at [[orthogonal group]]. Most links will go to the latter, even for $\mathrm{O}(p,q)$.

   I added another characterization of $Sp(n)$.

   I would be inclined to put all of the material at orthogonal group of an inner product space at orthogonal group. Most links will go to the latter, even for $\mathrm{O}(p,q)$.