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

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The group SO(5) is significant in particle physics, and its number of generators can be calculated using the formula N(N-1)/2. For SO(5), this results in 10 generators, as derived from the pattern established in lower dimensions. Specifically, SO(2) has 1 generator, SO(3) has 3, and SO(4) has 6. The explanation clarifies how rotations between axes contribute to the total count of generators. Understanding this calculation is essential for applications in theoretical physics.
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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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