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The Generalized Burnside Theorem in Noncommutative
DeformationT heory
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By
Eivind Eriksen
© 2011. Ashdin Publishing
Journal of Generalized Lie Theory and Applications (JGLTA), Volume 5
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Abstract
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Let A be an associative algebra over a field k, and let
M be a finite family of right A - modules. A study of
the noncommutative deformation functor Def
M of the family M leads to the construction of the algebra OA(M)
of observables and the generalized Burnside theorem, due to Laudal (2002). In this paper, we give an overview of
aspects of noncommutative deformations closely connected to the generalized Burnside theorem. |
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Phase Spaces and Deformation Theory
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By
Olav Arn © 2011. Ashdin Publishing
Journal of Generalized Lie Theory and Applications (JGLTA), Volume 5
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We have previously introduced the notion of non-commutative phase space (algebra) associated to any
associative algebra, defined over a field. The purpose of the present paper is to prove that this construction is useful
in non-commutative deformation theory for the construction of the versal family of finite families of modules. In
particular, we obtain a muchbetter understanding of the obstruction calculus, that is, of the Massey products. |
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Meandersand Frobenius Seaweed Lie Algebras
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By
Vincent Coll, Anthony Giaquinto, and Colton Magnan
© 2011. Ashdin Publishing
Journal of Generalized Lie Theory and Applications (JGLTA), Volume 5
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The index of a seaweed Lie algebra can be computed from its associated meander graph. We examine this
graph in several ways with a goal of determining families of Frobenius(index zero)seaweed algebras. Ouranalysis
gives two new families of Frobenius seaweed algebras as well as elementary proofs of known families of such Lie
algebras.
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Deformations of Complex 3-Dimensional Associative
Algebras
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By
Alice Fialowski, Michael Penkava, and Mitch Phillipson
© 2011. Ashdin Publishing
Journal of Generalized Lie Theory and Applications (JGLTA), Volume 5
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We study deformations and the moduli space of 3-dimensional complex associative algebras. We use
extensions to compute the moduli space, and then give a decomposition of this moduli space in to strata consisting of
complex projective orbifolds, glued together through jump deformations. The main purpose of this paper is to give
a logically organized description of the moduli space, and to give an explicit description of how the modulis paceis
constructed by extension. |
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On Graded Global Dimension of Color Hopf
Algebras
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By
Yan-Hua Wang
© 2011. Ashdin Publishing
Journal of Generalized Lie Theory and Applications (JGLTA), Volume 5
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In this paper, we prove the fundamental the orem of color Hopf modulesimilar to the fundamental the orem
of Hopf module. As an application, we prove that the graded global dimension of a color Hopf algebra coincides
with the projective dimension of the trivial module K.
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Some Properties of Intuitionistic Fuzzy Lie
Algebras over a Fuzzy Field
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By
P. L. Antony and P. L. Lilly © 2011. Ashdin Publishing
Journal of Generalized Lie Theory and Applications (JGLTA), Volume 5
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Abstract
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The concept of intuitionistic fuzzy Lie algebra over a fuzzy field is introduced. We study the "necessity"
and "possibility" operators on intuitionistic fuzzy Lie algebra over a fuzzy field and give some properties of
homomorphic images. |
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An Approachto Omni-Lie Algebroids using
Quasi-Derivations
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By
Dennise Garc © 2011. Ashdin Publishing
Journal of Generalized Lie Theory and Applications (JGLTA), Volume 5
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We introduce the notion of left (and right) quasi-Loday algebroids and a "universal space" for them,
called a left (right) omni-Loday algebroid, in such a way that Lie algebroids, omni-Lie algebras and omni-Loday
algebroids are particular substructures.
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Algebraic Structures Derived from Foams
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By
J.Scott Carter and Masahico Saito
© 2011. Ashdin Publishing
Journal of Generalized Lie Theory and Applications (JGLTA), Volume 5
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Foams are surfaces with branch lines at which three sheets merge. They have been used in the categorification
of sl(3) quantum knot invariants and also in physics. The 2D-TQFT of surfaces, on the other hand,
is classified by means of commutative Frobenius algebras, where saddle points correspond to multiplication and
comultiplication.In this paper,we explore algebraic operations that branch lines derive under TQFT.Inparticular,we
investigate Lie bracket and bialgebra structures. Relations to the original Frobenius algebra structures are discussed
both algebraically and diagrammatically... |
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Stability of the Generalized Polar Decomposition
Method for the Approximation of the Matrix
Exponential
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By
Elham Nobaria, S.Mohammad Hosseini
© 2011. Ashdin Publishing
Journal of Generalized Lie Theory and Applications (JGLTA), Volume 5
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Abstract
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Generalized polar decomposition method (or briefly GPD method) has been introduced by Munthe-Kaas
and Zanna [5] to approximate the matrix exponential. In this paper, we investigate the numerical stability of that
method with respect to round off propagation. The numerical GPD method includes two parts: splitting of a matrix
Z ∈ g, a Lie algebra of matrices and computing exp(Z)v for a vector v.We show that the former is stable provided
that (Z) is not so large, while the latter is not stable in general except with some restrictions on the entries of the
matrix Z and the vector v... |
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A Closed Form Solution for Quantum Oscillator
Perturbations Using Lie Algebras
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By
Clark Alexander © 2011. Ashdin Publishing
Journal of Physical Mathematics (JPM), Volume 3
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We give a new solution to a well-known problem, that of computing perturbed eigenvalues for quantum
oscillators. This article is nearly self contained and begins with all the necessary algebraic tools to make the
subsequent calculations. We define a new family of Lie algebras relevant to making computations for perturbed
(anharmonic) oscillators, and show that the only two formally closed solutions are indeed harmonic oscillators
themselves.Through elementaryc ombinatorics and noncanonical forms of well-known Lie algebras, we are able to
obtain a fully closed form solution for perturbed eigenvalues to first order... |
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Difficulties in Diagnostic Staging of Human
African Trypanosomiasis
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By
Peter G. E. Kennedy © 2011. Ashdin Publishing
Journal of Neuroparasitology (JNP), Volume 2
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Abstract
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Human African trypanosomiasis (HAT), also
known as sleeping sickness, continues to be a major hazard
to human health in 36 countries in sub-Saharan Africa. One
of the most important problems in disease management
is the considerable difficulty in distinguishing the early
(hemolymphatic) from the late (encephalitic) stage when
the parasites have crossed the blood-brain barrier to enter the
Central Nervous System(CNS). Treatment of the two stages
is different with the highly toxic arsenical drug melarsoprol
being the most commonly used therapy for CNS disease... |
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Keywords
Human African trypanosomiasis; sleeping
sickness; central nervous system (CNS); cerebrospinal
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Detection of Toxoplasma DNA in the Peripheral
Bloodof HIV-Positive Patients with
Neuro-opportunistic Infections by a Real-Time PCR
Assay
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By
Nestor Cardona, Natalia Basto, Beatriz Parra, Andres Felipe Zea, CarlosA.Pardo, Anilza Bonelo,
and Jorge Enrique Gomez-Marin
© 2011. Ashdin Publishing
Journal of Neuroparasitology (JNP), Volume 2
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Abstract
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We determine if peripheral blood sample could
be used for diagnosis of cerebral toxoplasmosis by a
real-time PCR assay and we analyzed the clinical and
laboratory findings in 22 patients with confirmed cerebral
toxoplasmosis compared to 27 patients with other neuroopportunistic infections. We compared two genet argets (B1
and RE) in the Taqman-PCR real-time assay. Efficiency
values were also calculated. We found that 18.8% (4/22)
of cases with cerebral toxoplasmosis and 7.4% (2/27) of
patients with other neuroinfections had positive results with
the Taqman PCR assay... |
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Keywords
Toxoplasma; cerebral toxoplasmosis; HIV;
Colombia; real-time PCR
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Neurologic Manifestations of Leishmania spp.
Infection
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By
ChristineAnne Petersen and M. Heather West Greenlee © 2011. Ashdin Publishing
Journal of Neuroparasitology (JNP), Volume 2
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Abstract
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When listing common clinical signs of the spectra
of Leishmania-derived diseases, neurologic malfunctions
are not commonly included. Despite this, there are multiple
reported instances both in human and veterinary medicine
where neurologic manifestations, whether central or
peripheral, are described. In this review, we describe
neurologic manifestations seen during infection with
Leishmania spp. with some discussion of the implicit effect
of inflammation on the blood brain barrier in both medical
and veterinary cases... |
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Keywords
Keywords leishmaniasis; neurologic; ocular; CNS; macrophage
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Implication of Uncoupling Protein 2 in Immunity to
Herpes Simplex Virus Type I in Resistant and
Susceptible Mouse Strains
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By
Laurie Rouger, Yan Sergerie, Denis Arsenijevic, Eric Paradis, Guy Boivin, and Denis Richard
© 2011. Ashdin Publishing
Journal of Neuroparasitology (JNP), Volume 2
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Abstract
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The present results demonstrate resistance to
HSV-1 in C57Bl6 mice is associated with differential
temporal body weight and GSH changes, compared to
susceptible 129Sv mouse strain. Strong brain viral load TK
and TLR-2 induction in the brain precedes TNF-α, iNOS,
IkBα and UCP2 expression in 129Sv mice. Interestingly,
we observe that UCP2 brain expression differs: UCP2 is
found in higher quantities in the mid and hind brain in
susceptible mice and in the forebrain in resistant mice.
In contrast with previous data, UCP2 KO mice did not
show differences in terms of survival, inflammatory gene
expression and neurodegeneration compared to their WT
controls... |
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Keywords
Mitochondrial transporters/exchangers; antioxidant;
encephalitis; brain; microglial cells
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Method to Investigate Contusion Mechanics in
Living Humans
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By
Geoffrey T. Desmoulin and GailS. Anderson
© 2011. Ashdin Publishing
Journal of Forensic Biomechanics, Volume 2
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Abstract
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The method utilizes equipment designed to
determine variables, which influence bruising mechanics
in living human subjects. The device allows weights to be
dropped in a controlled manner onto an impactor lying on
the skin surface to measure and analyze bruise mechanics.
Measured impact characteristics included peak force, peak
pressure, impact displacement, tissue stiffness, impact
velocity, pressure impulse, force impulse, kinetic energy
and the energy transmitted through the limb. Using kinetic
energy, transmitted energy and area in contact with the
skin we estimated energy absorbed by the limb and energy
density (J/m2)... |
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Keywords
Forensic science; contusion; bruise; biomechanics
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