Properties
The special unitary group SU(n) is a real matrix Lie group of dimension n2 − 1. Topologically, it is compact and simply connected. Algebraically, it is a simple Lie group (meaning its Lie algebra is simple; see below). The center of SU(n) is isomorphic to the cyclic group Zn. Its outer automorphism group, for n ≥ 3, is Z2, while the outer automorphism group of SU(2) is the trivial group.
The Lie algebra of SU(n), denoted by su(n) is generated by n2 operators, which satisfy the commutator relationship (for i, j, k, ℓ = 1, 2, ..., n)
Additionally, the operator
satisfies
which implies that the number of independent generators is n2 − 1.
Read more about this topic: Special Unitary Group
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