526 research outputs found
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 induces a transformation of .
We study the C*-algebra generated by this operator together with the algebra of
continuous functions which acts as multiplication operators on .
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 -theory of these algebras and use it to
compute the -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 on two generators such
that the norm of the sum of the generators and their inverses is bounded by
. These -constrained representations determine a C*-algebra
for each . We prove that these C*-algebras form a
continuous bundle of C*-algebras over 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
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