Ga. Elliott et M. Rordam, THE AUTOMORPHISM GROUP OF THE IRRATIONAL ROTATION C-ASTERISK-ALGEBRA, Communications in Mathematical Physics, 155(1), 1993, pp. 3-26
The structure of the automorphism group of a simple C-algebra of real
rank zero which is an inductive limit of circle algebras is described
. In particular, it is proved that the automorphism group of the irrat
ional rotation C-algebra, A(theta), for any irrational number theta,
is an extension of a topologically simple group by GL2(Z).