Group Actions. Spin group.

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The notion of symmetry is encoded in the notion of permutation representations. In this video, we introduce a useful and important reformulation of this concept, via group actions. The regular, and conjugation actions are introduced. We finish the video by looking at the simplest example of the spin group. In particular, we obtain a richer understanding of rotations in 3-dimensional space.
  1. DanielChanMaths
  2. Daniel Chan
  3. mathematics
  4. algebra
  5. group theory
  6. group actions
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Комментарии
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The permutation on the infinite set is what I never thought about before. It's great to know that.

haolinli
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Im a physics grad student that's been bluffing my way through every conversation about doing groups, I'm glad I finally understand them better

thomasmurphy
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Lovely explanations for the group action, and the little trick at the end was incredibly intuitive. I would say a better title is: "Group Actions. SU(2) group.", since you didn't focus on what exactly a spin group is, but rather what the SU(2) group is (not talking about the higher forms that don't share the same properties as SU(2)). Of course, with limited time, covering everything is not possible, so perhaps my slight criticism is unwarranted. In any case, great informative video!

sidrocksinthisworld
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Not only is Daniel great at explaining the math, but it is clear that he might have missed his calling to be a contortionist.

jmbg