130,684 research outputs found
Artin-Schelter regular algebras of dimension five with two generators
We study and classify Artin-Schelter regular algebras of dimension five with
two generators under an additional -grading by Hilbert driven
Gr\"{o}bner basis computations. All the algebras we obtained are strongly
noetherian, Auslander regular, and Cohen-Macaulay. One of the results provides
an answer to Fl{\o}ystad-Vatne's question in the context of -grading. Our results also achieve a connection between Lyndon words and
Artin-Schelter regular algebras.Comment: 32 page
Regularity criterion and classification for algebras of Jordan type
We show that Artin-Schelter regularity of a -graded algebra can
be examined by its associated -graded algebra. We prove that
there is exactly one class of four-dimensional Artin-Schelter regular algebras
with two generators of degree one in the Jordan case. This class is strongly
noetherian, Auslander regular, and Cohen-Macaulay. Their automorphisms and
point modules are described.Comment: 24 page
The structure of connected (graded) Hopf algebras
In this paper, we establish a structure theorem for connected graded Hopf
algebras over a field of characteristic by claiming the existence of a
family of homogeneous generators and a total order on the index set that
satisfy some desirable conditions. The approach to the structure theorem is
constructive, based on the combinatorial properties of Lyndon words and the
standard bracketing on words. As a surprising consequence of the structure
theorem, we show that connected graded Hopf algebras of finite Gelfand-Kirillov
dimension over a field of characteristic are all iterated Hopf Ore
extensions of the base field. In addition, some keystone facts of connected
Hopf algebras over a field of characteristic are observed as corollaries of
the structure theorem, without the assumptions of having finite
Gelfand-Kirillov dimension (or affineness) on Hopf algebras or of that the base
field is algebraically closed.Comment: 25 pages, add more details on some proof
Nakayama automorphisms of twisted tensor products
In this paper, we study homological properties of twisted tensor products of
connected graded algebras. We focus on the Ext-algebras of twisted tensor
products with a certain form of twisting maps firstly. We show those
Ext-algebras are also twisted tensor products, and depict the twisting maps for
such Ext-algebras in-depth. With those preparations, we describe Nakayama
automorphisms of twisted tensor products of noetherian Artin-Schelter regular
algebras
The Black Hole Mass and Magnetic Field Correlation in Active Galactic Nuclei
The observed optical luminosity in 5100 angstorm and black hole mass
correlation is used to probe the magnetic field of black holes harbored in
active galactic nuclei(AGNs). The model is based on the assumption that the
disk is heated by energy injection due to the magnetic coupling(MC) process and
the gravitational dissipation due to accretion. The MC process can transfer
energy and angular momentum from a rotating Kerr black hole to its surrounding
disk. The relation of optical luminosity in 5100 angstorm and black hole mass
as functions of the spin and magnetic field of the black hole is modelled. The
model predicts that optical luminosity in 5100 angstorm emitted from the disk
is sensitive to the strength of the poloidal component of the magnetic field on
the BH horizon. Based on the observations of optical luminosity in 5100
angstorm for 143 AGN sources, we obtain the correlation between mass and
magnetic field of black hole. And we compared out result with the approximate
result between mass and magnetic field of black hole derived from the condition
in the standard accretion disc theory.Comment: 7 pages, 4 figures, accepted by Chinese Journal of Astronomy and
Astrophysics, 2004 Supplement
Behavior of the Auslander condition with respect to regradings
We show that a noetherian ring graded by an abelian group of finite rank
satisfies the Auslander condition if and only if it satisfies the graded
Auslander condition. In addition, we also study the injective dimension, the
global dimension and the Cohen-Macaulay property from the same perspective of
that for the Auslander condtion. A key step of our approach is to establish
homological relations between a graded ring , its quotient ring modulo the
ideal and its localization ring with respect to the Ore set , where is a homogeneous regular normal
non-invertible element of .Comment: 23 page
Quantum resonances and decay of a chaotic fractal repeller observed using microwaves
The quantum resonances of classically chaotic n-disk geometries were studied
experimentally utilizing thin 2-D microwave geometries. The experiments yield
the frequencies and widths of low-lying resonances, which are compared with
semiclassical calculations. The longtime or small energy behavior of the
wave-vector auto-correlation gives information about the quantum decay rate,
which is in good agreement with that obtained from classical scattering theory.
The intermediate energy behavior shows non-universal oscillations determined by
periodic orbits.Comment: 5 pages, 3 eps figs include
Skew Calabi-Yau property of normal extensions
We prove that the skew Calabi-Yau property is preserved under normal
extension for locally finite positively graded algebras. We also obtain a
homological identity which describes the relationship between the Nakayama
automorphisms of skew Calabi-Yau locally finite positively graded algebras and
their normal extensions. As a preliminary, we show that the Nakayama
automorphisms of skew Calabi-Yau algebras always send a regular normal element
to a multiple of itself by a unit.Comment: 14 page
Homological Integral of Hopf Algebras
The left and right homological integrals are introduced for a large class of
infinite dimensional Hopf algebras. Using the homological integrals we prove a
version of Maschke's theorem for infinite dimensional Hopf algebras. The
generalization of Maschke's theorem and homological integrals are the keys to
study noetherian regular Hopf algebras of Gelfand-Kirillov dimension one.Comment: 30 page
Radial Velocity Studies of Close Binary Stars.V
Radial-velocity measurements and sine-curve fits to the orbital velocity
variations are presented for the fifth set of ten close binary systems: V376
And, EL Aqr, EF Boo, DN Cam, FN Cam, V776 Cas, SX Crv, V351 Peg, EQ Tau, KZ
Vir. All systems are double-lined spectroscopic contact binaries (KZ Vir may be
a low inclination, close, non-contact binary), with seven (all except EL Aqr,
SX Crv and EQ Tau) being the recent photometric discoveries of the Hipparcos
satellite project. The most interesting object is SX Crv, a contact system with
an unprecedently low mass ratio, q=0.066+/-0.003, whose existence challenges
the current theory of tidal stability of contact systems. Several of the
studied systems are prime candidates for combined light and radial-velocity
synthesis solutions.Comment: aastex5.0, 3 figures in PS; submitted to Astron.
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