How do I calculate number of generators of SO(5)?

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SUMMARY

The number of generators of the special orthogonal group SO(5) is calculated using the formula N(N-1)/2, where N represents the dimension of the group. For SO(5), this results in 10 generators. This formula derives from the ability to rotate axes within the group, specifically allowing for rotations from axis 1 to axes 2 through N, and similarly for other axes. The calculations for smaller groups are also confirmed: SO(2) has 1 generator, SO(3) has 3, and SO(4) has 6.

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  • Basic knowledge of rotational symmetries in physics
  • Awareness of the special orthogonal group notation (SO(n))
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This discussion is beneficial for mathematicians, physicists, and students studying group theory, particularly those interested in the applications of SO(n) groups in particle physics and rotational symmetries.

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The group SO(5) is relevant at times in particle physics. Can anybody please explain how to calculate the number of generators of SO(5)?
 
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With SO(n), you can rotate axis 1 into axes 2, 3,...,N. With axis 2, you can rotate it into 3,...N. So, SO(n) has (N-1)+(N-2)+...+1 = N(N-1)/2 generators. So, SO(2) has 1, SO(3) has 3, SO(4) has 6 and SO(5) has 10. Hope this helps.
 
Thanks a lot for your reply. I understand this now.
 

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