The study of abelian subalgebras of a finite dimensional semisimple Lie algebra has an ancient root. In 1945, \textit{A. I. Mal'tsev} [Izv. Akad. Nauk SSSR, Ser. Mat. 9, 291--300 (1945; Zbl 0063.03728)] found the maximal dimension of the abelian subalgebras of a finite dimensional simple Lie algebra. Also in 1965, \textit{B. Kostant} [Topology 3, Suppl. 2, 147--159 (1965; Zbl 0134.03504)] found a connection between the abelian subalgebras of a finite dimensional semisimple Lie algebra \(\mathcal{G}\) and the eigenvalues of a Casimir element acting on the exterior algebra \(\Lambda\mathcal{G}\). Moreover, a result due to D. Peterson says that there is a one-to-one correspondence between the abelian ideals of a Borel subalgebra of a finite dimensional simple Lie algebra and the so-called ``minuscule'' elements of the corresponding affine Weyl group. Also, \textit{D. Panyushev} and \textit{G. Röhrle} [Adv. Math. 159, No. 2, 229--246 (2001; Zbl 0993.22016)] found a natural bijection between maximal abelian ideals of a Borel subalgebra of a finite dimensional simple Lie algebra and long simple roots. In [Invent. Math. 156, No. 1, 175--221 (2004; Zbl 1112.17012)], \textit{R. Suter} described the abelian ideals of a Borel subalgebra of a finite dimensional complex simple Lie algebra. In the paper under review, the author describes the automorphism group of the poset \(\mathfrak{U}(\mathfrak{b})\) of abelian ideals of a Borel subalgebra \(\mathfrak{b}\) in a finite dimensional complex simple Lie algebra. The author shows that this automorphism group is isomorphic to the one of the corresponding Dynkin diagram other than for type \(C_3\). The author also describes the automorphism group of the Hasse diagram of \(\mathfrak{U}(\mathfrak{b})\). This automorphism group has also been described by Suter [loc. cit.] using a geometric approach.