2,304 research outputs found
Serre Theorem for involutory Hopf algebras
We call a monoidal category a Serre category if for any ,
such that C\ot D is semisimple, and are
semisimple objects in . Let be an involutory Hopf algebra,
, two -(co)modules such that is (co)semisimple as a
-(co)module. If (resp. ) is a finitely generated projective
-module with invertible Hattory-Stallings rank in then (resp. )
is (co)semisimple as a -(co)module. In particular, the full subcategory of
all finite dimensional modules, comodules or Yetter-Drinfel'd modules over
the dimension of which is invertible in are Serre categories.Comment: a new version: 8 page
Tame group actions on central simple algebras
We study actions of linear algebraic groups on finite-dimensional central
simple algebras. We describe the fixed algebra for a broad class of such
actions.Comment: 19 pages, LaTeX; slightly revised; final version will appear in
Journal of Algebr
Representations and -theory of Discrete Groups
Let be a discrete group of finite virtual cohomological dimension
with certain finiteness conditions of the type satisfied by arithmetic groups.
We define a representation ring for , determined on its elements of
finite order, which is of finite type. Then we determine the contribution of
this ring to the topological -theory , obtaining an exact
formula for the difference in terms of the cohomology of the centralizers of
elements of finite order in .Comment: 4 page
X-ray sources and their optical counterparts in the globular cluster M 22
Using XMM-Newton EPIC imaging data, we have detected 50 low-luminosity X-ray
sources in the field of view of M 22, where 5 +/- 3 of these sources are likely
to be related to the cluster. Using differential optical photometry, we have
identified probable counterparts to those sources belonging to the cluster.
Using X-ray spectroscopic and timing studies, supported by the optical colours,
we propose that the most central X-ray sources in the cluster are cataclysmic
variables, millisecond pulsars, active binaries and a blue straggler. We also
identify a cluster of galaxies behind this globular cluster.Comment: 11 pages, 7 figures, accepted for publication in A&
Extended diffeomorphism algebras in (quantum) gravitational physics
We construct an explicit representation of the algebra of local
diffeomorphisms of a manifold with realistic dimensions. This is achieved in
the setting of a general approach to the (quantum) dynamics of a physical
system which is characterized by the fundamental role assigned to a basic
underlying symmetry. The developed mathematical formalism makes contact with
the relevant gravitational notions by means of the addition of some extra
structure. The specific manners in which this is accomplished, together with
their corresponding physical interpretation, lead to different gravitational
models. Distinct strategies are in fact briefly outlined, showing the
versatility of the present conceptual framework.Comment: 20 pages, LATEX, no figure
Affine algebraic groups with periodic components
A connected component of an affine algebraic group is called periodic if all
its elements have finite order. We give a characterization of periodic
components in terms of automorphisms with finite number of fixed points. It is
also discussed which connected groups have finite extensions with periodic
components. The results are applied to the study of the normalizer of a maximal
torus in a simple algebraic group.Comment: 20 page
Harmonic analysis and the Riemann-Roch theorem
This paper is a continuation of papers: arXiv:0707.1766 [math.AG] and
arXiv:0912.1577 [math.AG]. Using the two-dimensional Poisson formulas from
these papers and two-dimensional adelic theory we obtain the Riemann-Roch
formula on a projective smooth algebraic surface over a finite field.Comment: 7 pages; to appear in Doklady Mathematic
Polynomial identity rings as rings of functions
We generalize the usual relationship between irreducible Zariski closed
subsets of the affine space, their defining ideals, coordinate rings, and
function fields, to a non-commutative setting, where "varieties" carry a
PGL_n-action, regular and rational "functions" on them are matrix-valued,
"coordinate rings" are prime polynomial identity algebras, and "function
fields" are central simple algebras of degree n. In particular, a prime
polynomial identity algebra of degree n is finitely generated if and only if it
arises as the "coordinate ring" of a "variety" in this setting. For n = 1 our
definitions and results reduce to those of classical affine algebraic geometry.Comment: 24 pages. This is the final version of the article, to appear in J.
Algebra. Several proofs have been streamlined, and a new section on
Brauer-Severi varieties has been adde
Tribological and corrosion wear of graphite ring against Ti6Al4V disk in artificial sea water
Severe degradations result from the friction of two antagonists in sea water environment. It is proposed to evaluate materials resistance to wear with a tribocorrosion experimental set-up which is mechanically and electrochemically instrumented. The method is illustrated with graphite and Ti6Al4V.The deposition of graphite on Ti6Al4V samples is observed and modifies the contact characteristics. Processes of graphite wear due to mechanical effect are characterised. Observations clearly indicate that Ti6Al4V degradations depend on the electrochemical potential imposed and more precisely on the electrochemical conditions in the contact zone
A Novel Hybrid CNN-AIS Visual Pattern Recognition Engine
Machine learning methods are used today for most recognition problems.
Convolutional Neural Networks (CNN) have time and again proved successful for
many image processing tasks primarily for their architecture. In this paper we
propose to apply CNN to small data sets like for example, personal albums or
other similar environs where the size of training dataset is a limitation,
within the framework of a proposed hybrid CNN-AIS model. We use Artificial
Immune System Principles to enhance small size of training data set. A layer of
Clonal Selection is added to the local filtering and max pooling of CNN
Architecture. The proposed Architecture is evaluated using the standard MNIST
dataset by limiting the data size and also with a small personal data sample
belonging to two different classes. Experimental results show that the proposed
hybrid CNN-AIS based recognition engine works well when the size of training
data is limited in siz
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