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Lie bracket of a matrix Lie group Updated 2025-07-16
Because the Lie bracket has to be a bilinear map, all we need to do to specify it uniquely is to specify how it acts on every pair of some basis of the Lie algebra.
Then, together with the Baker-Campbell-Hausdorff formula and the Lie group-Lie algebra correspondence, this forms an exceptionally compact description of a Lie group.
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The first Bitcoin exchange. Coded as a hack, and they didn't manage to fix the hacks as the site evolved in a major way, which led to massive hacks.
Their creation is clearly visible on the archive history of bitcoin.org: web.archive.org/web/20100701000000*/bitcoin.org which started having massively more archives since Mt. Gox opened.
One parameter subgroup Updated 2025-07-16
The one parameter subgroup of a Lie group for a given element of its Lie algebra is a subgroup of given by:
Intuitively, is a direction, and is how far we move along a given direction. This intuition is especially vivid in for example in the case of the Lie algebra of , the rotation group.
One parameter subgroups can be seen as the continuous analogue to the cycle of an element of a group.
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Wikipedia mentions quoting his Nobel Prize biography:
There are unlisted articles, also show them or only show them.