The Recognition Theorem For Graded Lie Algebras In Prime Characteristic

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The Recognition Theorem for Graded Lie Algebras in Prime Characteristic

Georgia Benkart,Thomas Bradford Gregory,Alexander Premet
The Recognition Theorem for Graded Lie Algebras in Prime Characteristic Book PDF

Author : Georgia Benkart,Thomas Bradford Gregory,Alexander Premet
Publisher : American Mathematical Soc.
Page : 145 pages
File Size : 41,8 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821842263

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The Recognition Theorem for Graded Lie Algebras in Prime Characteristic by Georgia Benkart,Thomas Bradford Gregory,Alexander Premet Pdf

The ``Recognition Theorem'' for graded Lie algebras is an essential ingredient in the classification of finite-dimensional simple Lie algebras over an algebraically closed field of characteristic $p>3$. The main goal of this monograph is to present the first complete proof of this fundamental result.

Simple Lie Algebras Over Fields of Positive Characteristic: Classifying the absolute toral rank two case

Helmut Strade
Simple Lie Algebras Over Fields of Positive Characteristic Classifying the absolute toral rank two case Book PDF

Author : Helmut Strade
Publisher : Walter de Gruyter
Page : 392 pages
File Size : 44,5 Mb
Release : 2004
Category : Mathematics
ISBN : 9783110197013

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Simple Lie Algebras Over Fields of Positive Characteristic: Classifying the absolute toral rank two case by Helmut Strade Pdf

The problem of classifying the finite-dimensional simple Lie algebras over fields of characteristic p > 0 is a long-standing one. Work on this question during the last 45 years has been directed by the Kostrikin-Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p > 5 a finite-dimensional restricted simple Lie algebra is classical or of Cartan type. This conjecture was proved for p > 7 by Block and Wilson in 1988. The generalization of the Kostrikin-Shafarevich Conjecture for the general case of not necessarily restricted Lie algebras and p > 7 was announced in 1991 by Strade and Wilson and eventually proved by Strade in 1998. The final Block-Wilson-Strade-Premet Classification Theorem is a landmark result of modern mathematics and can be formulated as follows: Every finite-dimensional simple Lie algebra over an algebraically closed field of characteristic p > 3 is of classical, Cartan, or Melikian type. In the three-volume book, the author is assembling the proof of the Classification Theorem with explanations and references. The goal is a state-of-the-art account on the structure and classification theory of Lie algebras over fields of positive characteristic leading to the forefront of current research in this field. This is the second part of the three-volume book about the classification of the simple Lie algebras over algebraically closed fields of characteristics > 3. The first volume contains the methods, examples, and a first classification result. This second volume presents insight in the structure of tori of Hamiltonian and Melikian algebras. Based on sandwich element methods due to Aleksei. I. Kostrikin and Alexander A. Premet and the investigation of absolute toral rank 2 simple Lie algebras over algebraically closed fields of characteristics > 3 is given.

Simple Lie Algebras Over Fields of Positive Characteristic: Structure theory

Helmut Strade
Simple Lie Algebras Over Fields of Positive Characteristic Structure theory Book PDF

Author : Helmut Strade
Publisher : Walter de Gruyter
Page : 548 pages
File Size : 49,9 Mb
Release : 2004
Category : Mathematics
ISBN : 9783110142112

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Simple Lie Algebras Over Fields of Positive Characteristic: Structure theory by Helmut Strade Pdf

The problem of classifying the finite-dimensional simple Lie algebras over fields of characteristic p > 0 is a long-standing one. Work on this question during the last 45 years has been directed by the Kostrikin-Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p > 5 a finite-dimensional restricted simple Lie algebra is classical or of Cartan type. This conjecture was proved for p > 7 by Block and Wilson in 1988. The generalization of the Kostrikin-Shafarevich Conjecture for the general case of not necessarily restricted Lie algebras and p > 7 was announced in 1991 by Strade and Wilson and eventually proved by Strade in 1998. The final Block-Wilson-Strade-Premet Classification Theorem is a landmark result of modern mathematics and can be formulated as follows: Every finite-dimensional simple Lie algebra over an algebraically closed field of characteristic p > 3 is of classical, Cartan, or Melikian type. In the three-volume book, the author is assembling the proof of the Classification Theorem with explanations and references. The goal is a state-of-the-art account on the structure and classification theory of Lie algebras over fields of positive characteristic leading to the forefront of current research in this field. This first volume is devoted to preparing the ground for the classification work to be performed in the second and third volume. The concise presentation of the general theory underlying the subject matter and the presentation of classification results on a subclass of the simple Lie algebras for all odd primesmake this volume an invaluable source and reference for all research mathematicians and advanced graduate students in albegra.

Classifying the Absolute Toral Rank Two Case

Helmut Strade
Classifying the Absolute Toral Rank Two Case Book PDF

Author : Helmut Strade
Publisher : Walter de Gruyter GmbH & Co KG
Page : 394 pages
File Size : 41,5 Mb
Release : 2017-04-10
Category : Mathematics
ISBN : 9783110517606

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Classifying the Absolute Toral Rank Two Case by Helmut Strade Pdf

The problem of classifying the finite dimensional simple Lie algebras over fields of characteristic p > 0 is a long standing one. Work on this question has been directed by the Kostrikin Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p > 5 a finite dimensional restricted simple Lie algebra is classical or of Cartan type. This conjecture was proved for p > 7 by Block and Wilson in 1988. The generalization of the Kostrikin-Shafarevich Conjecture for the general case of not necessarily restricted Lie algebras and p > 7 was announced in 1991 by Strade and Wilson and eventually proved by Strade in 1998. The final Block-Wilson-Strade-Premet Classification Theorem is a landmark result of modern mathematics and can be formulated as follows: Every simple finite dimensional simple Lie algebra over an algebraically closed field of characteristic p > 3 is of classical, Cartan, or Melikian type. This is the second part of a three-volume book about the classification of the simple Lie algebras over algebraically closed fields of characteristic > 3. The first volume contains the methods, examples and a first classification result. This second volume presents insight in the structure of tori of Hamiltonian and Melikian algebras. Based on sandwich element methods due to A. I. Kostrikin and A. A. Premet and the investigations of filtered and graded Lie algebras, a complete proof for the classification of absolute toral rank 2 simple Lie algebras over algebraically closed fields of characteristic > 3 is given. Contents Tori in Hamiltonian and Melikian algebras 1-sections Sandwich elements and rigid tori Towards graded algebras The toral rank 2 case

Representations of Algebraic Groups, Quantum Groups, and Lie Algebras

Representations of Algebraic Groups AMS-IMS-SIAM Joint Summer Research Conference, Quantum Groups
Representations of Algebraic Groups Quantum Groups and Lie Algebras Book PDF

Author : Representations of Algebraic Groups AMS-IMS-SIAM Joint Summer Research Conference, Quantum Groups
Publisher : American Mathematical Soc.
Page : 270 pages
File Size : 41,6 Mb
Release : 2006
Category : Affine algebraic groups
ISBN : 9780821839249

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Representations of Algebraic Groups, Quantum Groups, and Lie Algebras by Representations of Algebraic Groups AMS-IMS-SIAM Joint Summer Research Conference, Quantum Groups Pdf

Covers various aspects of the representation theory of Lie algebras, finite groups of Lie types, Hecke algebras, and Lie super algebras. This book outlines connections among irreducible representations of certain blocks of reduced enveloping algebras of semi-simple Lie algebras in positive characteristic.

The Generalised Jacobson-Morosov Theorem

Peter O'Sullivan
The Generalised Jacobson Morosov Theorem Book PDF

Author : Peter O'Sullivan
Publisher : American Mathematical Soc.
Page : 135 pages
File Size : 43,9 Mb
Release : 2010-08-06
Category : Mathematics
ISBN : 9780821848951

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The Generalised Jacobson-Morosov Theorem by Peter O'Sullivan Pdf

The author considers homomorphisms $H \to K$ from an affine group scheme $H$ over a field $k$ of characteristic zero to a proreductive group $K$. Using a general categorical splitting theorem, Andre and Kahn proved that for every $H$ there exists such a homomorphism which is universal up to conjugacy. The author gives a purely group-theoretic proof of this result. The classical Jacobson-Morosov theorem is the particular case where $H$ is the additive group over $k$. As well as universal homomorphisms, the author considers more generally homomorphisms $H \to K$ which are minimal, in the sense that $H \to K$ factors through no proper proreductive subgroup of $K$. For fixed $H$, it is shown that the minimal $H \to K$ with $K$ reductive are parametrised by a scheme locally of finite type over $k$.

Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups

Drew Armstrong
Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups Book PDF

Author : Drew Armstrong
Publisher : American Mathematical Soc.
Page : 176 pages
File Size : 51,6 Mb
Release : 2009-10-08
Category : Mathematics
ISBN : 9780821844908

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Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups by Drew Armstrong Pdf

This memoir is a refinement of the author's PhD thesis -- written at Cornell University (2006). It is primarily a desription of new research but also includes a substantial amount of background material. At the heart of the memoir the author introduces and studies a poset $NC^{(k)}(W)$ for each finite Coxeter group $W$ and each positive integer $k$. When $k=1$, his definition coincides with the generalized noncrossing partitions introduced by Brady and Watt in $K(\pi, 1)$'s for Artin groups of finite type and Bessis in The dual braid monoid. When $W$ is the symmetric group, the author obtains the poset of classical $k$-divisible noncrossing partitions, first studied by Edelman in Chain enumeration and non-crossing partitions.

Lie Algebras and Related Topics

Georgia Benkart
Lie Algebras and Related Topics Book PDF

Author : Georgia Benkart
Publisher : American Mathematical Soc.
Page : 313 pages
File Size : 41,9 Mb
Release : 1990
Category : Mathematics
ISBN : 9780821851197

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Lie Algebras and Related Topics by Georgia Benkart Pdf

The 1984 classification of the finite-dimensional restricted simple Lie algebras over an algebraically closed field of characteristic $p>7$ provided the impetus for a Special Year of Lie Algebras, held at the University of Wisconsin, Madison, during 1987-88. Work done during the Special Year and afterward put researchers much closer toward a solution of the long-standing problem of determining the finite-dimensional simple Lie algebras over an algebraically closed field of characteristic $p>7$. This volume contains the proceedings of a conference on Lie algebras and related topics, held in May 1988 to mark the end of the Special Year. The conference featured lectures on Lie algebras of prime characteristic, algebraic groups, combinatorics and representation theory, and Kac-Moody and Virasoro algebras. Many facets of recent research on Lie theory are reflected in the papers presented here, testifying to the richness and diversity of this topic.

Sum Formula for SL2 Over a Totally Real Number Field

Roelof W. Bruggeman,Roberto J. Miatello
Sum Formula for SL2 Over a Totally Real Number Field Book PDF

Author : Roelof W. Bruggeman,Roberto J. Miatello
Publisher : American Mathematical Soc.
Page : 81 pages
File Size : 43,7 Mb
Release : 2009-01-21
Category : Mathematics
ISBN : 9780821842027

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Sum Formula for SL2 Over a Totally Real Number Field by Roelof W. Bruggeman,Roberto J. Miatello Pdf

The authors prove a general form of the sum formula $\mathrm{SL}_2$ over a totally real number field. This formula relates sums of Kloosterman sums to products of Fourier coefficients of automorphic representations. The authors give two versions: the spectral sum formula (in short: sum formula) and the Kloosterman sum formula. They have the independent test function in the spectral term, in the sum of Kloosterman sums, respectively.

Asymptotic Expansions for Infinite Weighted Convolutions of Heavy Tail Distributions and Applications

Ph Barbe,William P. McCormick
Asymptotic Expansions for Infinite Weighted Convolutions of Heavy Tail Distributions and Applications Book PDF

Author : Ph Barbe,William P. McCormick
Publisher : American Mathematical Soc.
Page : 117 pages
File Size : 52,5 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821842591

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Asymptotic Expansions for Infinite Weighted Convolutions of Heavy Tail Distributions and Applications by Ph Barbe,William P. McCormick Pdf

The authors establish some asymptotic expansions for infinite weighted convolution of distributions having regularly varying tails. Applications to linear time series models, tail index estimation, compound sums, queueing theory, branching processes, infinitely divisible distributions and implicit transient renewal equations are given.A noteworthy feature of the approach taken in this paper is that through the introduction of objects, which the authors call the Laplace characters, a link is established between tail area expansions and algebra. By virtue of this representation approach, a unified method to establish expansions across a variety of problems is presented and, moreover, the method can be easily programmed so that a computer algebra package makes implementation of the method not only feasible but simple.

Compactification of the Drinfeld Modular Surfaces

Thomas Lehmkuhl
Compactification of the Drinfeld Modular Surfaces Book PDF

Author : Thomas Lehmkuhl
Publisher : American Mathematical Soc.
Page : 113 pages
File Size : 40,5 Mb
Release : 2009-01-21
Category : Science
ISBN : 9780821842447

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Compactification of the Drinfeld Modular Surfaces by Thomas Lehmkuhl Pdf

In this article the author describes in detail a compactification of the moduli schemes representing Drinfeld modules of rank 2 endowed with some level structure. The boundary is a union of copies of moduli schemes for Drinfeld modules of rank 1, and its points are interpreted as Tate data. The author also studies infinitesimal deformations of Drinfeld modules with level structure.

Hypocoercivity

CŽdric Villani
Hypocoercivity Book PDF

Author : CŽdric Villani
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 42,9 Mb
Release : 2009-10-08
Category : Mathematics
ISBN : 9780821844984

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Hypocoercivity by CŽdric Villani Pdf

This memoir attempts at a systematic study of convergence to stationary state for certain classes of degenerate diffusive equations, taking the general form ${\frac{\partial f}{\partial t}}+ L f =0$. The question is whether and how one can overcome the degeneracy by exploiting commutators.

Center Manifolds for Semilinear Equations with Non-Dense Domain and Applications to Hopf Bifurcation in Age Structured Models

Pierre Magal,Shigui Ruan
Center Manifolds for Semilinear Equations with Non Dense Domain and Applications to Hopf Bifurcation in Age Structured Models Book PDF

Author : Pierre Magal,Shigui Ruan
Publisher : American Mathematical Soc.
Page : 84 pages
File Size : 54,6 Mb
Release : 2009
Category : Bifurcation theory
ISBN : 9780821846537

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Center Manifolds for Semilinear Equations with Non-Dense Domain and Applications to Hopf Bifurcation in Age Structured Models by Pierre Magal,Shigui Ruan Pdf

Several types of differential equations, such as delay differential equations, age-structure models in population dynamics, evolution equations with boundary conditions, can be written as semilinear Cauchy problems with an operator which is not densely defined in its domain. The goal of this paper is to develop a center manifold theory for semilinear Cauchy problems with non-dense domain. Using Liapunov-Perron method and following the techniques of Vanderbauwhede et al. in treating infinite dimensional systems, the authors study the existence and smoothness of center manifolds for semilinear Cauchy problems with non-dense domain. As an application, they use the center manifold theorem to establish a Hopf bifurcation theorem for age structured models.

Yang-Mills Connections on Orientable and Nonorientable Surfaces

Nan-Kuo Ho,Chiu-Chu Melissa Liu
Yang Mills Connections on Orientable and Nonorientable Surfaces Book PDF

Author : Nan-Kuo Ho,Chiu-Chu Melissa Liu
Publisher : American Mathematical Soc.
Page : 113 pages
File Size : 55,8 Mb
Release : 2009-10-08
Category : Mathematics
ISBN : 9780821844915

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Yang-Mills Connections on Orientable and Nonorientable Surfaces by Nan-Kuo Ho,Chiu-Chu Melissa Liu Pdf

In ``The Yang-Mills equations over Riemann surfaces'', Atiyah and Bott studied Yang-Mills functional over a Riemann surface from the point of view of Morse theory. In ``Yang-Mills Connections on Nonorientable Surfaces'', the authors study Yang-Mills functional on the space of connections on a principal $G_{\mathbb{R}}$-bundle over a closed, connected, nonorientable surface, where $G_{\mathbb{R}}$ is any compact connected Lie group. In this monograph, the authors generalize the discussion in ``The Yang-Mills equations over Riemann surfaces'' and ``Yang-Mills Connections on Nonorientable Surfaces''. They obtain explicit descriptions of equivariant Morse stratification of Yang-Mills functional on orientable and nonorientable surfaces for non-unitary classical groups $SO(n)$ and $Sp(n)$.

Rock Blocks

Will Turner
Rock Blocks Book PDF

Author : Will Turner
Publisher : American Mathematical Soc.
Page : 117 pages
File Size : 55,9 Mb
Release : 2009-10-08
Category : Mathematics
ISBN : 9780821844625

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Rock Blocks by Will Turner Pdf

Consider representation theory associated to symmetric groups, or to Hecke algebras in type A, or to $q$-Schur algebras, or to finite general linear groups in non-describing characteristic. Rock blocks are certain combinatorially defined blocks appearing in such a representation theory, first observed by R. Rouquier. Rock blocks are much more symmetric than general blocks, and every block is derived equivalent to a Rock block. Motivated by a theorem of J. Chuang and R. Kessar in the case of symmetric group blocks of abelian defect, the author pursues a structure theorem for these blocks.