The special unitary group of degree n, denoted SU(n), is the group of n × n unitary matrices with determinant 1. (In general, unitary matrices have complex determinants with modulus 1 but arbitrary phase.) The group operation is that of matrix multiplication. The special unitary group is a subgroup of the unitary group U(n), consisting of all n × n unitary matrices, which is itself a subgroup of the general linear group GL(n, C).
The SU(n) groups find wide application in the Standard Model of particle physics, especially SU(2) in the electroweak interaction and SU(3) in QCD.
The simplest case, SU(1), is the trivial group, having only a single element. The group SU(2) 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), we have a surjective homomorphism from SU(2) to the rotation group SO(3) whose kernel is {+I, −I}.
Read more about Special Unitary Group: Properties, Generators, n = 2, n = 3, Lie Algebra, Generalized Special Unitary Group, Important Subgroups
Famous quotes containing the words special and/or group:
“The books may say that nine-month-olds crawl, say their first words, and are afraid of strangers. Your exuberantly concrete and special nine-month-old hasn’t read them. She may be walking already, not saying a word and smiling gleefully at every stranger she sees. . . . You can support her best by helping her learn what she’s trying to learn, not what the books say a typical child ought to be learning.”
—Amy Laura Dombro (20th century)
“I can’t think of a single supposedly Black issue that hasn’t wasted the original Black target group and then spread like the measles to outlying white experience.”
—June Jordan (b. 1936)