5 research outputs found
Torsion pairs and rigid objects in tubes
We classify the torsion pairs in a tube category and show that they are in
bijection with maximal rigid objects in the extension of the tube category
containing the Pruefer and adic modules. We show that the annulus geometric
model for the tube category can be extended to the larger category and
interpret torsion pairs, maximal rigid objects and the bijection between them
geometrically. We also give a similar geometric description in the case of the
linear orientation of a Dynkin quiver of type A.Comment: 25 pages, 13 figures. Paper shortened. Minor errors correcte
A remark on Leclerc's Frobenius categories
Leclerc recently studied certain Frobenius categories in connection with
cluster algebra structures on coordinate rings of intersections of opposite
Schubert cells. We show that these categories admit a description as Gorenstein
projective modules over an Iwanaga-Gorenstein ring of virtual dimension at most
two. This is based on a Morita type result for Frobenius categories.Comment: 5 pages, extended abstract for a talk at the Workshop Homological
Bonds between Commutative Algebra and Representation Theory at CRM Barcelona,
February 2015, comments welcom
Subword complexes, cluster complexes, and generalized multi-associahedra
In this paper, we use subword complexes to provide a uniform approach to
finite type cluster complexes and multi-associahedra. We introduce, for any
finite Coxeter group and any nonnegative integer k, a spherical subword complex
called multi-cluster complex. For k=1, we show that this subword complex is
isomorphic to the cluster complex of the given type. We show that multi-cluster
complexes of types A and B coincide with known simplicial complexes, namely
with the simplicial complexes of multi-triangulations and centrally symmetric
multi-triangulations respectively. Furthermore, we show that the multi-cluster
complex is universal in the sense that every spherical subword complex can be
realized as a link of a face of the multi-cluster complex.Comment: 26 pages, 3 Tables, 2 Figures; final versio
The complete ISO spectrum of NGC 6302
We present the combined Infrared Space Observatory Short-Wavelength
Spectrometer and Long-Wavelength Spectrometer 2.4--197 micron spectrum of the
Planetary Nebula NGC 6302 which contains in addition to strong atomic lines, a
series of emission features due to solid state components. The broad wavelength
coverage enables us to more accurately identify and determine the properties of
both oxygen- and carbon-rich circumstellar dust. A simple model fit was made to
determine the abundance and typical temperature of the amorphous silicates,
enstatite and forsterite. Forsterite and enstatite do have roughly the same
abundance and temperature. The origin and location of the dust in a toroidal
disk around the central star are discussed.Comment: 8 pages, 4 figures, accepted by A&A. The postscriptfile can also be
found at http://www.astro.uva.nl/~frankm/papers.htm