The special unitary group consists of complex matrices satisfying and

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Group theory and symmetry · Group theory and symmetry

Invariance, Ch Lie groups and Lie algebras: rotations, SU(2) and the double cover

Problem

The special unitary group

SU(4)

consists of

4\times4

complex matrices

U

satisfying

U^\dagger U = \mathsf{1}

and

\det U = 1

. Find the dimension of

SU(4)

as a Lie group, that is, the number of independent real parameters needed to specify

U

near the identity.