What is "special unitary group"

n. (context linear algebra group theory English) (l en a group of square unitary matrix unitary matrices with complex entries and determinant equal to one.)

In mathematics, the special unitary group of degree , denoted , is the Lie group of unitary matrices with determinant 1. The group operation is that of matrix multiplication. The special unitary group is a subgroup of the unitary group , consisting of all unitary matrices. As a compact classical group, is the group that preserves the standard inner product on . It is itself a subgroup of the general linear group, .

The groups find wide application in the Standard Model of particle physics, especially in the electroweak interaction and in quantum chromodynamics.

The simplest case, , is the trivial group, having only a single element. The group is isomorphic to the group of quaternions of norm 1, and is thus diffeomorphic to the 3-sphere. Since unit quaternions can be used to represent rotations in 3-dimensional space (up to sign), there is a surjective homomorphism from to the rotation group whose kernel is }. is also identical to one of the symmetry groups of spinors, Spin(3), that enables a spinor presentation of rotations.