On the Exponential of Matrices in su(4)
  This note presents explicit formulae for the exponentials of a wide variety of matrices which are 4x4, anti-Hermitian. Easily verifiable conditions characterizing when such matrices admit one of three minimal polynomials are also given. Essential use of the algebra isomorphism between real 4x4 matrices and the tensor product of the quaternions with themseleves is made. Illustrations from important applications are given. 
Viswanath Ramakrishna & Hong Zhou