  In [H. Duan and S. Liu, The isomorphism type of the centralizer of an element
in a Lie group, Journal of algebra, 376(2013), 25-45], we have determined the
isomorphism type of the centralizer of an element in a simpe Lie group. As a
sequel to [H. Duan and S. Liu, The isomorphism type of the centralizer of an
element in a Lie group, Journal of algebra, 376(2013), 25-45.] we present a
general procedure to calculate the isomorphism type of the fixed set of the
inverse involution on a Lie group.
