special unitary group

Noun
S^3 & \cong SU(2) = \text{Spin } 3 \\ 2 \bigg\downarrow & \\ SO(3) & \cong \mathbb{R}P^3 \end{align}$$
 * 1)  For given n, the group of n×n unitary matrices with complex elements and determinant equal to one.
 * 2) * 1992 [Prentice-Hall], George H. Duffey, Applied Group Theory: For Physicists and Chemists, 2015, Dover, Unabridged Republication, page 284,
 * The special unitary group in two dimensions is represented by the 2 X 2 unitary matrices whose determinants equal 1.
 * 1) * 2004, Roger Cooke (translator), Vladimir I. Arnold, Lectures on Partial Differential Equations, [1997, Lekstii ob uravneniyakh s chastnymi proizvodnymi], Springer, page 81,
 * When n = 3, the group of rotations SO(3) is isomorphic to the real three-dimensional projective space $$\mathbb{R}P^3$$. It has a two-sheeted covering by the three-dimensional sphere (the group of unit quaternions), which in turn is isomorphic to the special unitary group $$SU(2)$$, also known as the spin group of order 3, as in the following diagram:
 * $$\begin{align}
 * $$\begin{align}

Usage notes
Denoted SU(n). Each special unitary group is a Lie group and a subgroup of the unitary group U(n). SU(1) is the trivial group.

Translations

 * Finnish: erityinen unitaarinen ryhmä