C*-algebras associated with endomorphisms and polymorphisms of compact abelian groups

A surjective endomorphism or, more generally, a polymorphism in the sense of \cite{SV}, of a compact abelian group $H$ induces a transformation of $L^2(H)$. We study the C*-algebra generated by this operator together with the algebra of continuous functions $C(H)$ which acts as multiplication operators on $L^2(H)$. Under a natural condition on the endo- or polymorphism, this algebra is simple and can be described by generators and relations. In the case of an endomorphism it is always purely infinite, while for a polymorphism in the class we consider, it is either purely infinite or has a unique trace. We prove a formula allowing to determine the $K$-theory of these algebras and use it to compute the $K$-groups in a number of interesting examples.Comment: 25 page

Combinatorics of 1-particle irreducible n-point functions via coalgebra in quantum field theory

We give a coalgebra structure on 1-vertex irreducible graphs which is that of a cocommutative coassociative graded connected coalgebra. We generalize the coproduct to the algebraic representation of graphs so as to express a bare 1-particle irreducible n-point function in terms of its loop order contributions. The algebraic representation is so that graphs can be evaluated as Feynman graphs

Case Studies of Habitable Trojan Planets in the System of HD 23079

We investigate the possibility of habitable Trojan planets in the HD 23079 star-planet system. This system consists of a solar-type star and a Jupiter-type planet, which orbits the star near the outer edge of the stellar habitable zone in an orbit of low eccentricity. We find that in agreement with previous studies Earth-mass habitable Trojan planets are possible in this system, although the success of staying within the zone of habitability is significantly affected by the orbital parameters of the giant planet and by the initial condition of the theoretical Earth-mass planet. In one of our simulations, the Earth-mass planet is captured by the giant planet and thus becomes a habitable moon.Comment: 24 pages, 8 figures, 3 tables; International Journal of Astrobiology (in press

On C*-algebras related to constrained representations of a free group

We consider representations of the free group $F_2$ on two generators such that the norm of the sum of the generators and their inverses is bounded by $\mu\in[0,4]$. These $\mu$-constrained representations determine a C*-algebra $A_{\mu}$ for each $\mu\in[0,4]$. We prove that these C*-algebras form a continuous bundle of C*-algebras over $[0,4]$ and calculate their K-groups.Comment: 9 page

Orbital Stability of Planets in Binary Systems: A New Look at Old Results

About half of all known stellar systems with Sun-like stars consist of two or more stars, significantly affecting the orbital stability of any planet in these systems. This observational evidence has prompted a large array of theoretical research, including the derivation of mathematically stringent criteria for the orbital stability of planets in stellar binary systems, valid for the "coplanar circular restricted three-body problem". In the following, we use these criteria to explore the validity of results from previous theoretical studies.Comment: 3 pages, 1 figure; submitted to: Exoplanets: Detection, Formation and Dynamics, IAU Symposium 249, eds. Y.-S. Sun, S. Ferraz-Mello, and J.-L. Zhou (Cambridge: Cambridge University Press

Basal Chromospheric Flux and Maunder Minimum-type Stars: The quiet-Sun Chromosphere as a Universal Phenomenon

Aims: We demonstrate the universal character of the quiet-Sun chromosphere among inactive stars (solar-type and giants). By assessing the main physical processes, we shed new light on some common observational phenomena. Methods: We discuss measurements of the solar Mt. Wilson S-index, obtained by the Hamburg Robotic Telescope around the extreme minimum year 2009, and compare the established chromospheric basal Ca II K line flux to the Mt. Wilson S-index data of inactive ("flat activity") stars, including giants. Results: During the unusually deep and extended activity minimum of 2009, the Sun reached S-index values considerably lower than in any of its previously observed minima. In several brief periods, the Sun coincided exactly with the S-indices of inactive ("flat", presumed Maunder Minimum-type) solar analogues of the Mt. Wilson sample; at the same time, the solar visible surface was also free of any plages or remaining weak activity regions. The corresponding minimum Ca II K flux of the quiet Sun and of the presumed Maunder Minimum-type stars in the Mt. Wilson sample are found to be identical to the corresponding Ca II K chromospheric basal flux limit. Conclusions: We conclude that the quiet-Sun chromosphere is a universal phenomenon among inactive stars. Its mixed-polarity magnetic field, generated by a local, "fast" turbulent dynamo finally provides a natural explanation for the minimal soft X-ray emission observed for inactive stars. Given such a local dynamo also works for giant chromospheres, albeit on larger length scales, i.e., l ~ R/g, with R and g as stellar radius and surface gravity, respectively, the existence of giant spicular phenomena and the guidance of mechanical energy toward the acceleration zone of cool stellar winds along flux-tubes have now become traceable.Comment: 6 pages, 4 figures; Astronomy & Astrophysics (Research Note), in pres