Hyperbolic Unit Groups and Quaternion Algebras

We Classify the rational quadratic extensions K and the finite groups G for which the group ring R[G] of G over the ring R of integers of K has the property that the group of units of augmentation 1 of R[G] is hyperbolic. We also construct units in a non-split quaternion algebra over R.Comment: 15 pages, this work is part of the PHd. Thesis of the third author. The paper was accepted in Proceedings Mathematical Science

Publications of the planetary biology program for 1975: A special bibliography

The Planetary Biology Program of the National Aeronautics and Space Administration is the first and only integrated program to methodically investigate the planetary events which may have been responsible for, or related to, the origin, evolution, and distribution of life in the universe. Research supported by this program is divided into the seven areas listed below: (1) chemical evolution, (2) organic geochemistry, (3) life detection, (4) biological adaptation, (5) bioinstrumentation, (6) planetary environments, and (7) origin of life. The arrangement of references in this bibliography follows the division of research described above. Articles are listed alphabetically by author under the research area with which they are most closely related. Only those publications which resulted from research supported by the Planetary Biology Program and which bear a 1975 publication date have been included. Abstracts and theses are not included because of the preliminary and abbreviated nature of the former and the frequent difficulty of obtaining the latter

Correlated electrons systems on the Apollonian network

Strongly correlated electrons on an Apollonian network are studied using the Hubbard model. Ground-state and thermodynamic properties, including specific heat, magnetic susceptibility, spin-spin correlation function, double occupancy and one-electron transfer, are evaluated applying direct diagonalization and quantum Monte Carlo. The results support several types of magnetic behavior. In the strong-coupling limit, the quantum anisotropic spin 1/2 Heisenberg model is used and the phase diagram is discussed using the renormalization group method. For ferromagnetic coupling, we always observe the existence of long-range order. For antiferromagnetic coupling, we find a paramagnetic phase for all finite temperatures.Comment: 7 pages, 8 figure