Classification of direct limits of even Cuntz-circle algebras

We prove a classification theorem for purely infinte simple C*-algebras that is strong enough to show that the tensor products of two different irrational rotation algebras with the same even Cuntz algebra are isomorphic. In more detail, let C be be the class of simple C*-algebras A which are direct limits A = lim A_k, in which each A_k is a finite direct sum of algebras of the form C(X) \otimes M_n \otimes O_m, where m is even, O_m is the Cuntz algebra, X is either a point, a compact interval, or the circle S^1, and each map A_k ---> A is approximately absorbing. ("Approximately absorbing" is defined in Section 1 of the paper.) We show that two unital C*-algebras A and B in the class C are isomorphic if and only if (K_0 (A), [1_A], K_1 (A)) is isomorphic to (K_0 (B), [1_B], K_1 (B)). This class is large enough to exhaust all possible K-groups: if G_0 and G_1 are countable odd torsion groups and g is in G_0, then there is a C*-algebra A in C with (K_0 (A), [1_A], K_1 (A)) isomorphic to (G_0, g, G_1). The class C contains the tensor products of irrational rotation algebras with even Cuntz algebras. It is also closed under several natural operations.Comment: LaTeX, 71 pages (in 10pt type). This replacement corrects assorted misprints and is in smaller type. The paper has been accepted in the Memoirs of the AM

Explaining the observed velocity dispersion of dwarf galaxies by baryonic mass loss during the first collapse

In the widely adopted LambdaCDM scenario for galaxy formation, dwarf galaxies are the building blocks of larger galaxies. Since they formed at relatively early epochs when the background density was relatively high, they are expected to retain their integrity as satellite galaxies when they merge to form larger entities. Although many dwarf spheroidal galaxies (dSphs) are found in the galactic halo around the Milky Way, their phase space density (or velocity dispersion) appears to be significantly smaller than that expected for satellite dwarf galaxies in the LambdaCDM scenario. In order to account for this discrepancy, we consider the possibility that they may have lost a significant fraction of their baryonic matter content during the first infall at the Hubble expansion turnaround. Such mass loss arises naturally due to the feedback by relatively massive stars which formed in their centers briefly before the maximum contraction. Through a series of N-body simulations, we show that the timely loss of a significant fraction of the dSphs initial baryonic matter content can have profound effects on their asymptotic half-mass radius, velocity dispersion, phase-space density, and the mass fraction between residual baryonic and dark matter.Comment: 6 pages, 6 figures, accepted for publication in the Ap