The faithful linear representation of least degree ofS n andA n over a field of characteristic 2

1976 ◽  
Vol 151 (2) ◽  
pp. 127-137 ◽  
Author(s):  
Ascher Wagner
Keyword(s):  
Linear Representation ◽  
Faithful Linear Representation ◽  
Characteristic 2

scholarly journals REDUCIBILITY OF THE COHEN–WALES REPRESENTATION OF THE ARTIN GROUP OF TYPE Dn

2012 ◽  
Vol 21 (10) ◽  
pp. 1250071 ◽  
Author(s):  
CLAIRE LEVAILLANT
Keyword(s):  
Root System ◽  
Linear Representation ◽  
Computer Assisted ◽  
Artin Group ◽  
Type D ◽  
Faithful Linear Representation ◽  
Positive Roots

We construct a linear representation of the CGW algebra of type Dn. This representation has degree n2 - n, the number of positive roots of a root system of type Dn. We show that the representation is generically irreducible, but that when the parameters of the algebra are related in a certain way, it becomes reducible. As a representation of the Artin group of type Dn, this representation is equivalent to the faithful linear representation of Cohen–Wales. We give a reducibility criterion for this representation as well as a conjecture on the semisimplicity of the CGW algebra of type Dn. Our proof is computer-assisted using Mathematica.

scholarly journals Linear representations of random groups

2019 ◽  
Vol 09 (03) ◽  
pp. 1950016
Author(s):  
Gady Kozma ◽  
Alexander Lubotzky
Keyword(s):  
Linear Representation ◽  
Linear Representations ◽  
Faithful Linear Representation ◽  
Random Groups

We show that for a fixed [Formula: see text], Gromov random groups with any density [Formula: see text] have no nontrivial degree [Formula: see text] representations over any field, a.a.s. This is especially interesting in light of the results of Agol, Ollivier and Wise that when [Formula: see text] such groups have a faithful linear representation over [Formula: see text], a.a.s.

scholarly journals Faithful linear representations of certain free nilpotent groups

1995 ◽  
Vol 37 (1) ◽  
pp. 33-36 ◽  
Author(s):  
B. A. F. Wehrfritz
Keyword(s):  
Free Groups ◽  
Linear Representation ◽  
Nilpotent Groups ◽  
Finite Degree ◽  
Final Comment ◽  
Linear Representations ◽  
Variety Of Groups ◽  
Countable Rank ◽  
Faithful Linear Representation ◽  
Finitary Linear

Brian Hartley asked me whether a free (nilpotent of class 2 and exponent p2)-group of countable rank has a faithful linear representation of finite degree, p here being a prime of course. The answer is yes. The point is that this then yields via work of F. Leinen and M. J. Tomkinson, see [3,3.6] an image of a linear p-group, which is not even finitary linear. The question of which relatively free groups have faithful linear representations dates back at least to work of W. Magnus in the 1930's, see [4, pp. 33, 34 and the final comment on p. 40] for a discussion of this. Our construction, which works more generally, is a further contribution. We write ℜc for the variety of nilpotent groups of class at most c and (ℭ9 for the variety of groups of exponent dividing q.

scholarly journals Noncomplete affine structures on Lie algebras of maximal class

2002 ◽  
Vol 29 (2) ◽  
pp. 71-77 ◽  
Author(s):  
E. Remm ◽  
Michel Goze
Keyword(s):  
Lie Algebra ◽  
Linear Representation ◽  
Heisenberg Algebra ◽  
Maximal Class ◽  
Affine Structure ◽  
Nilpotent Lie Algebra ◽  
3 Dimensional ◽  
Faithful Linear Representation ◽  
Affine Structures ◽  
Filiform Lie Algebra

Every affine structure on Lie algebra𝔤defines a representation of𝔤inaff(ℝn). If𝔤is a nilpotent Lie algebra provided with a complete affine structure then the corresponding representation is nilpotent. We describe noncomplete affine structures on the filiform Lie algebraLn. As a consequence we give a nonnilpotent faithful linear representation of the 3-dimensional Heisenberg algebra.

scholarly journals A New Inverted Topp-Leone Distribution: Applications to the COVID-19 Mortality Rate in Two Different Countries

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 25 ◽  
Author(s):  
Ehab Almetwally ◽  
Randa Alharbi ◽  
Dalia Alnagar ◽  
Eslam Hafez
Keyword(s):  
Statistical Model ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Likelihood Estimation ◽  
Linear Representation ◽  
Rate Function ◽  
Estimation Methods ◽  
Unknown Parameters ◽  
Least Squares Estimators ◽  
New Distribution

This paper aims to find a statistical model for the COVID-19 spread in the United Kingdom and Canada. We used an efficient and superior model for fitting the COVID 19 mortality rates in these countries by specifying an optimal statistical model. A new lifetime distribution with two-parameter is introduced by a combination of inverted Topp-Leone distribution and modified Kies family to produce the modified Kies inverted Topp-Leone (MKITL) distribution, which covers a lot of application that both the traditional inverted Topp-Leone and the modified Kies provide poor fitting for them. This new distribution has many valuable properties as simple linear representation, hazard rate function, and moment function. We made several methods of estimations as maximum likelihood estimation, least squares estimators, weighted least-squares estimators, maximum product spacing, Crame´r-von Mises estimators, and Anderson-Darling estimators methods are applied to estimate the unknown parameters of MKITL distribution. A numerical result of the Monte Carlo simulation is obtained to assess the use of estimation methods. also, we applied different data sets to the new distribution to assess its performance in modeling data.

scholarly journals Two algebraic deformations of a K3 surface

1981 ◽  
Vol 82 ◽  
pp. 1-26
Author(s):  
Daniel Comenetz
Keyword(s):  
Hyperelliptic Curve ◽  
Double Cover ◽  
Rational Curves ◽  
K3 Surface ◽  
Quartic Surface ◽  
Quadric Cone ◽  
Birational Model ◽  
Affine Line ◽  
Characteristic 2 ◽  
General Member

Let X be a nonsingular algebraic K3 surface carrying a nonsingular hyperelliptic curve of genus 3 and no rational curves. Our purpose is to study two algebraic deformations of X, viz. one specialization and one generalization. We assume the characteristic ≠ 2. The generalization of X is a nonsingular quartic surface Q in P3 : we wish to show in § 1 that there is an irreducible algebraic family of surfaces over the affine line, in which X is a member and in which Q is a general member. The specialization of X is a surface Y having a birational model which is a ramified double cover of a quadric cone in P3.

scholarly journals Germline Transformation of Drosophila virilis With the Transposable Element mariner

Genetics ◽  
1996 ◽  
Vol 143 (1) ◽  
pp. 365-374 ◽  
Author(s):  
Allan R Lohe ◽  
Daniel L Hartl
Keyword(s):  
Transposable Element ◽  
Common Ancestor ◽  
Pcr Amplification ◽  
Drosophila Virilis ◽  
Cell Region ◽  
Diverse Species ◽  
Drosophila Mauritiana ◽  
Characteristic 2 ◽  
In Situ Hybridizations

Abstract An important goal in molecular genetics has been to identify a transposable element that might serve as an efficient transformation vector in diverse species of insects. The transposable element mariner occurs naturally in a wide variety of insects. Although virtually all mariner elements are nonfunctional, the Mosl element isolated from Drosophila mauritiana is functional. Mosl was injected into the pole-cell region of embryos of D. virilis, which last shared a common ancestor with D. mauritiana 40 million years ago. Mosl PCR fragments were detected in several pools of DNA from progeny of injected animals, and backcross lines were established. Because Go lines were pooled, possibly only one transformation event was actually obtained, yielding a minimum frequency of 4%. Mosl segregated in a Mendelian fashion, demonstrating chromosomal integration. The copy number increased by spontaneous mobilization. In situ hybridization confirmed multiple polymorphic locations of Mosl. Integration results in a characteristic 2-bp TA duplication. One Mosl element integrated into a tandem array of 370-bp repeats. Some copies may have integrated into heterochromatin, as evidenced by their ability to support PCR amplification despite absence of a signal in Southern and in situ hybridizations.

scholarly journals EXAMPLES OF FINITE-DIMENSIONAL POINTED HOPF ALGEBRAS IN CHARACTERISTIC 2

2020 ◽  
pp. 1-14
Author(s):  
NICOLÁS ANDRUSKIEWITSCH ◽  
DIRCEU BAGIO ◽  
SARADIA DELLA FLORA ◽  
DAIANA FLÔRES
Keyword(s):  
Hopf Algebras ◽  
Abelian Groups ◽  
Vector Spaces ◽  
Group Algebras ◽  
Finite Abelian Groups ◽  
Finite Dimensional ◽  
Pointed Hopf Algebras ◽  
Characteristic 2 ◽  
Nichols Algebras ◽  
Kirillov Dimension

Abstract We present new examples of finite-dimensional Nichols algebras over fields of characteristic 2 from braided vector spaces that are not of diagonal type, admit realizations as Yetter–Drinfeld modules over finite abelian groups, and are analogous to Nichols algebras of finite Gelfand–Kirillov dimension in characteristic 0. New finite-dimensional pointed Hopf algebras over fields of characteristic 2 are obtained by bosonization with group algebras of suitable finite abelian groups.

scholarly journals On the existence of some specific elements in finite fields of characteristic 2

2012 ◽  
Vol 18 (4) ◽  
pp. 800-813 ◽  
Author(s):  
Peipei Wang ◽  
Xiwang Cao ◽  
Rongquan Feng
Keyword(s):  
Finite Fields ◽  
Characteristic 2
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