The complex analogue of the special orthogonal group, i.e. the subgroup of the unitary group with determinant equals exactly 1 instead of an arbitrary complex number with absolute value equal 1 as is the case for the unitary group.
Double cover of .
Isomorphic to the quaternions.
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The special unitary group is .
The Special Unitary Group, denoted as \( \text{SU}(n) \), is a significant mathematical structure in the field of group theory, particularly in the study of symmetries and quantum mechanics.