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Ryan Budney
Ryan Budney
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A nice way to look at the 4-dimensional rotation matrices SO(4)$SO_4$ is that it's universal cover is isomorphic to S^3 x S^3$S^3 \times S^3$. The map S^3 x S^3 --> SO(4)$S^3 \times S^3 \to SO_4$ is given by left and right quaternionic multiplication by a unit vectors.

A nice way to look at the 4-dimensional rotation matrices SO(4) is that it's universal cover is isomorphic to S^3 x S^3. The map S^3 x S^3 --> SO(4) is given by left and right quaternionic multiplication by a unit vectors.

A nice way to look at the 4-dimensional rotation matrices $SO_4$ is that it's universal cover is isomorphic to $S^3 \times S^3$. The map $S^3 \times S^3 \to SO_4$ is given by left and right quaternionic multiplication by a unit vectors.

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Ryan Budney
Ryan Budney
  • 44.3k
  • 2
  • 139
  • 245

A nice way to look at the 4-dimensional rotation matrices SO(4) is that it's universal cover is isomorphic to S^3 x S^3. The map S^3 x S^3 --> SO(4) is given by left and right quaternionic multiplication by a unit vectors.