Special unitary group

English

Noun

1. Template:Lb For 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.

   • Template:Quote-book
   • 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 $ℝP^3$. 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:

     $\begin{array}{cc}{S}^3& \cong SU(2)=\text{Spin }3\\ 2\downarrow & \\ SO(3)& \cong ℝP^3\end{array}$

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: Template:T