3,827 research outputs found
Representations of Hopf Ore extensions of group algebras and pointed Hopf algebras of rank one
In this paper, we study the representation theory of Hopf-Ore extensions of
group algebras and pointed Hopf algebras of rank one over an arbitrary field
. Let H=kG(\chi, a,\d) be a Hopf-Ore extension of and a rank one
quotient Hopf algebra of , where is a field, is a group, is a
central element of and is a -valued character for with
. We first show that the simple weight modules over and
are finite dimensional. Then we describe the structures of all simple weight
modules over and , and classify them. We also consider the
decomposition of the tensor product of two simple weight modules over into
the direct sum of indecomposable modules. Furthermore, we describe the
structures of finite dimensional indecomposable weight modules over and
, and classify them. Finally, when is a primitive -th root of
unity for some , we determine all finite dimensional indecomposable
projective objects in the category of weight modules over .Comment: arXiv admin note: substantial text overlap with arXiv:1206.394
Effects of tidally enhanced stellar wind on the horizontal branch morphology of globular clusters
Metallicity is the first parameter to influence the horizontal branch (HB)
morphology of globular clusters (GCs). It has been found, however, that some
other parameters may also play an important role in affecting the morphology.
While the nature of these important parameters remains unclear, they are
believed to be likely correlated with wind mass-loss of red giants, since this
mass loss determines their subsequent locations on the HB. Unfortunately, the
mass loss during the red giant stages of the stellar evolution is poorly
understood at present. The stellar winds of red giants may be tidally enhanced
by companion stars if they are in binary systems. We investigate evolutionary
consequences of red giants in binaries by including tidally enhanced stellar
winds, and examine the effects on the HB morphology of GCs. We find that red,
blue, and extreme horizontal branch stars are all produced under the effects of
tidally enhanced stellar wind without any additional assumptions on the
mass-loss dispersion. Furthermore, the horizontal branch morphology is found to
be insensitive to the tidal enhancement parameter, Bw. We compare our
theoretical results with the observed horizontal branch morphology of globular
cluster NGC 2808, and find that the basic morphology of the horizontal branch
can be well reproduced. The number of blue horizontal branch stars in our
calculations, however, is lower than that of NGC 2808.Comment: 7 pages, 4 figures, 2 tables, accepted for publication in Astronomy &
Astrophysic
Majorana corner modes and flat-band Majorana edge modes in superconductor/topological-insulator/superconductor junctions
Recently, superconductors with higher-order topology have stimulated
extensive attention and research interest. Higher-order topological
superconductors exhibit unconventional bulk-boundary correspondence, thus allow
exotic lower-dimensional boundary modes, such as Majorana corner and hinge
modes. However, higher-order topological superconductivity has yet to be found
in naturally occurring materials. In this work, we investigate higher-order
topology in a two-dimensional Josephson junction comprised of two -wave
superconductors separated by a topological insulator thin film. We found that
zero-energy Majorana corner modes, a boundary fingerprint of higher-order
topological superconductivity, can be achieved by applying magnetic field. When
an in-plane Zeeman field is applied to the system, two corner states appear in
the superconducting junction. Furthermore, we also discover a two dimensional
nodal superconducting phase which supports flat-band Majorana edge modes
connecting the bulk nodes. Importantly, we demonstrate that zero-energy
Majorana corner modes are stable when increasing the thickness of topological
insulator thin film.Comment: 9 pages, 4 figure
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