In SU ( 2 ) gauge theory in 4 dimensional Minkowski space, a gauge transformation corresponds to a choice of an element of the special unitary group SU ( 2 ) at each point in spacetime.
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A similar three angle decomposition applies to SU ( 2 ), the special unitary group of rotations in complex 2D space, with the difference that " ? " ranges from 0 to 2?.
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The center of the special unitary group has order gcd ( " n, q " + 1 ) and consists of those unitary scalars which also have order dividing " n ".
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The Vandermonde polynomial can be considered a special case of the Weyl character formula, specifically the Weyl denominator formula ( the case of the trivial representation ) of the special unitary group SU ( n ).
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To make this more explicit, there are two approaches : the group can either be identified with the group Sp ( 1 ) of unit quaternions, or with the special unitary group SU ( 2 ).
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The corresponding Lie groups are the noncompact group \ mathrm { SL } ( 2, \ mathbb C ) of real matrices with the unit determinant and the special unitary group \ mathrm { SU } ( 2 ), which is compact.
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The quotient of the unitary group by its center is called the "'projective unitary group "',, and the quotient of the special unitary group by its center is the "'projective special unitary group " '.
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The quotient of the unitary group by its center is called the "'projective unitary group "',, and the quotient of the special unitary group by its center is the "'projective special unitary group " '.
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For example, projective representations of the 3-dimensional rotation group, which is the special orthogonal group SO ( 3 ), are ordinary representations of the special unitary group SU ( 2 ) ( see Representation theory of SU ( 2 ) ).
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Important subgroups of each U ( " N " ) are those unitary matrices which have unit determinant ( or are " unimodular " ) : these are called the special unitary groups and are denoted SU ( " N " ).
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