advanced_tools:group_theory:sp_1
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advanced_tools:group_theory:sp_1 [2023/04/17 03:31] edi [Concrete] |
advanced_tools:group_theory:sp_1 [2025/03/08 21:32] (current) edi [Concrete] |
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| **Representations** | **Representations** | ||
| - | The diagram below shows the defining representation of $Sp(1)$ in its upper branch and the (3-dimensional) adjoint representation of the same group in the lower branch. The latter representation can be used to rotate objects in 3D space and has applications in computer graphics. For a more detailed explanation of this diagram and representations of other Lie groups see [[https://esackinger.wordpress.com/blog/lie-groups-and-their-representations/#sp1_quaternion|Fun with Symmetry]]. | + | The diagram below shows the defining representation of $Sp(1)$ in its upper branch and the (3-dimensional) adjoint representation of the same group in the lower branch. The latter representation can be used to rotate objects in 3D space and has applications in computer graphics. For a more detailed explanation of this diagram and representations of other Lie groups see [[https://esackinger.wordpress.com/rotation-in-3-dimensions-and-angular-momentum/#sp1|Fun with Symmetry]]. |
| [{{ :advanced_tools:group_theory:representation_theory:sp1_quaternions.jpg?nolink }}] | [{{ :advanced_tools:group_theory:representation_theory:sp1_quaternions.jpg?nolink }}] | ||
advanced_tools/group_theory/sp_1.txt ยท Last modified: 2025/03/08 21:32 by edi
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