eli5 what is lie algebra?
In: Mathematics
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Well, an ELI5 explanation of group theory is not going to be as completely correct as the [Wikipedia article](https://en.wikipedia.org/wiki/Lie_algebra), but here goes.
If you have a vector space, for example the 3D space we’re using to compute a video game scene, certain transformations have unique properties. One such transformation is rotation. If you have a 3D object in this space and you rotate it, you’ll notice some interesting properties. If you rotate a football in the real world, you can cast shadows of many different shapes (from on end the shadow is circular when from the side it’s clearly not circular). Regardless of these different “shapes you see” the football “remains the same shape” when all three dimensions are considered.
A Lie group, in this example, would be all the possible position/rotation/orientations in which the football can be placed. The Lie algebra is the transformation that rotates the football from where it starts to the orientation it ends up in.
By the way, the Lie is a name (named after the inventor, Marius Sophus Lie, like many math concepts) and it’s pronounced “Lee”.
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