In his 2008 paper published in the Canadian Journal of Mathematics, F. Boca investigates an AF algebra A, whose Bratteli diagram arises from the Farey–Stern–Brocot sequence. It turns out that A coincides with the AF algebra M1 introduced in 1988 by the present author in a paper published in Advances in Mathematics. We give a procedure to recognize A among all ﬁnitely presented AF algebras whose Murray–von Neumann order of projections is a lattice. Further: (i) A is a *-subalgebra of Glimm universal algebra; (ii) tracial states of A correspond to Borel probability measures on the unit real interval; (iii) all primitive ideals of A are essential; (iv) the automorphism group of A has exactly two connected components.
Cite this article
Daniele Mundici, Recognizing the Farey–Stern–Brocot AF algebra. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 20 (2009), no. 4, pp. 327–338