special unitary group

plural special unitary groups

1. group theoryFor given n, the group of n×n unitary matrices with complex elements and determinant equal to one.

   1992 [Prentice-Hall], George H. Duffey, Applied Group Theory: For Physicists and Chemists, 2015, Dover, Unabridged Republication, page 284, The special unitary group in two dimensions is represented by the 2 X 2 unitary matrices whose determinants equal 1.

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   The group is called the special unitary group in two dimensions, or SU(2), because it acts on matrices of degree 2.

   2000, Herbert S. Green, Information Theory and Quantum Physics: Physical Foundations for Understanding the Conscious Process, Springer, page 26

   2004, Roger Cooke (translator), Vladimir I. Arnold, Lectures on Partial Differential Equations, [1997, Lekstii ob uravneniyakh s chastnymi proizvodnymi], Springer, page 81, When n = 3, the group of rotations SO(3) is isomorphic to the real three-dimensional projective space ℝP³. It has a two-sheeted covering by the three-dimensional sphere (the group of unit quaternions), which in turn is isomorphic to the special unitary group SU(2), also known as the spin group of order 3, as in the following diagram