Polynomial Rings and Affine Algebraic Geometry: Praag 2018, Tokyo, Japan, February 12-16, Kuroda Shigeru, Onoda Nobuharu, Freudenburg Gene
Автор: Karel Dekimpe Название: Almost-Bieberbach Groups: Affine and Polynomial Structures ISBN: 3540618996 ISBN-13(EAN): 9783540618997 Издательство: Springer Рейтинг: Цена: 41880.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Starting from basic knowledge of nilpotent (Lie) groups, an algebraic theory of almost-Bieberbach groups, the fundamental groups of infra-nilmanifolds, is developed in this work.
Автор: Amitai Regev, Antonio Giambruno, Claudio Procesi, Eli Aljadeff Название: Rings with Polynomial Identities and Finite Dimensional Representations of Algebras ISBN: 1470451743 ISBN-13(EAN): 9781470451745 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 82770.00 T Наличие на складе: Нет в наличии. Описание: A polynomial identity for an algebra (or a ring) $A$ is a polynomial in noncommutative variables that vanishes under any evaluation in $A$. An algebra satisfying a nontrivial polynomial identity is called a PI algebra, and this is the main object of study in this book, which can be used by graduate students and researchers alike. The book is divided into four parts. Part 1 contains foundational material on representation theory and noncommutative algebra. In addition to setting the stage for the rest of the book, this part can be used for an introductory course in noncommutative algebra. An expert reader may use Part 1 as reference and start with the main topics in the remaining parts. Part 2 discusses the combinatorial aspects of the theory, the growth theorem, and Shirshov's bases. Here methods of representation theory of the symmetric group play a major role. Part 3 contains the main body of structure theorems for PI algebras, theorems of Kaplansky and Posner, the theory of central polynomials, M. Artin's theorem on Azumaya algebras, and the geometric part on the variety of semisimple representations, including the foundations of the theory of Cayley-Hamilton algebras. Part 4 is devoted first to the proof of the theorem of Razmyslov, Kemer, and Braun on the nilpotency of the nil radical for finitely generated PI algebras over Noetherian rings, then to the theory of Kemer and the Specht problem. Finally, the authors discuss PI exponent and codimension growth. This part uses some nontrivial analytic tools coming from probability theory. The appendix presents the counterexamples of Golod and Shafarevich to the Burnside problem.
Автор: Mora Название: Solving Polynomial Equation Systems III ISBN: 0521811554 ISBN-13(EAN): 9780521811552 Издательство: Cambridge Academ Рейтинг: Цена: 121440.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This third volume of four describes all the most important techniques, mainly based on Groebner bases. It covers the `standard` solutions (Gianni-Kalkbrener, Auzinger-Stetter, Cardinal-Mourrain) as well as the more innovative (Lazard-Rouillier, Giusti-Heintz-Pardo). The author also explores the historical background, from Bezout to Macaulay.
Автор: David A. Cox Название: Applications of Polynomial Systems ISBN: 1470451379 ISBN-13(EAN): 9781470451370 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 49330.00 T Наличие на складе: Нет в наличии. Описание: Systems of polynomial equations can be used to model an astonishing variety of phenomena. This book explores the geometry and algebra of such systems and includes numerous applications. The book begins with elimination theory from Newton to the twenty-first century and then discusses the interaction between algebraic geometry and numerical computations, a subject now called numerical algebraic geometry. The final three chapters discuss applications to geometric modeling, rigidity theory, and chemical reaction networks in detail. Each chapter ends with a section written by a leading expert.Examples in the book include oil wells, HIV infection, phylogenetic models, four-bar mechanisms, border rank, font design, Stewart-Gough platforms, rigidity of edge graphs, Gaussian graphical models, geometric constraint systems, and enzymatic cascades. The reader will encounter geometric objects such as Bezier patches, Cayley-Menger varieties, and toric varieties; and algebraic objects such as resultants, Rees algebras, approximation complexes, matroids, and toric ideals. Two important subthemes that appear in multiple chapters are toric varieties and algebraic statistics. The book also discusses the history of elimination theory, including its near elimination in the middle of the twentieth century.The main goal is to inspire the reader to learn about the topics covered in the book. With this in mind, the book has an extensive bibliography containing over 350 books and papers.
Автор: Kaarli, Kalle , Pixley, Alden F. Название: Polynomial Completeness in Algebraic Systems ISBN: 0367398338 ISBN-13(EAN): 9780367398330 Издательство: Taylor&Francis Рейтинг: Цена: 65320.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
Boolean algebras have historically played a special role in the development of the theory of general or universal algebraic systems, providing important links between algebra and analysis, set theory, mathematical logic, and computer science. It is not surprising then that focusing on specific properties of Boolean algebras has lead to new directions in universal algebra.
In the first unified study of polynomial completeness, Polynomial Completeness in Algebraic Systems focuses on and systematically extends another specific property of Boolean algebras: the property of affine completeness. The authors present full proof that all affine complete varieties are congruence distributive and that they are finitely generated if and only if they can be presented using only a finite number of basic operations. In addition to these important findings, the authors describe the different relationships between the properties of lattices of equivalence relations and the systems of functions compatible with them. An introductory chapter surveys the appropriate background material, exercises in each chapter allow readers to test their understanding, and open problems offer new research possibilities. Thus Polynomial Completeness in Algebraic Systems constitutes an accessible, coherent presentation of this rich topic valuable to both researchers and graduate students in general algebraic systems.
Автор: Masuda Kayo Et Al Название: Affine Algebraic Geometry - Proceedings Of The Conference ISBN: 9814436690 ISBN-13(EAN): 9789814436694 Издательство: World Scientific Publishing Рейтинг: Цена: 126720.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The present volume grew out of an international conference on affine algebraic geometry held in Osaka, Japan during 3-6 March 2011 and is dedicated to Professor Masayoshi Miyanishi on the occasion of his 70th birthday. It contains 16 refereed articles in the areas of affine algebraic geometry, commutative algebra and related fields, which have been the working fields of Professor Miyanishi for almost 50 years. Readers will be able to find recent trends in these areas too. The topics contain both algebraic and analytic, as well as both affine and projective, problems. All the results treated in this volume are new and original which subsequently will provide fresh research problems to explore. This volume is suitable for graduate students and researchers in these areas.
Автор: Chun-Ju Lai, Li Luo, Weiqiang Wang, Yiqiang Li, Zhaobing Fan Название: Affine Flag Varieties and Quantum Symmetric Pairs ISBN: 1470441756 ISBN-13(EAN): 9781470441753 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 80390.00 T Наличие на складе: Нет в наличии. Описание: Demonstrates that the quantum groups arising from Lusztig algebras and Schur algebras via stabilization procedures are (idempotented) coideal subalgebras of quantum groups of affine $\mathfrak{sl}$ and $\mathfrak{gl}$ types, respectively. In this way, the authors provide geometric realizations of eight quantum symmetric pairs of affine types.
Автор: Bogdan Ion, Siddhartha Sahi Название: Double Affine Hecke Algebras and Congruence Groups ISBN: 1470443260 ISBN-13(EAN): 9781470443269 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 71060.00 T Наличие на складе: Нет в наличии.
Автор: Oliver Lorscheid, Thorsten Weist Название: Quiver Grassmannians of Extended Dynkin Type $D$: Part I: Schubert Systems and Decompositions into Affine Spaces ISBN: 1470436477 ISBN-13(EAN): 9781470436476 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 83160.00 T Наличие на складе: Нет в наличии. Описание: The authors characterize the affine spaces in terms of the combinatorics of a fixed coefficient quiver for $M$. The method of proof is to exhibit explicit equations for the Schubert cells of $\mathrm{Gr}_{\underline{e}}(M)$ and to solve this system of equations successively in linear terms.
Автор: Elizabeth Milicevic, Petra Schwer, Anne Thomas Название: Dimensions of Affine Deligne-Lusztig Varieties: A New Approach Via Labeled Folded Alcove Walks and Root Operators ISBN: 1470436760 ISBN-13(EAN): 9781470436766 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 67710.00 T Наличие на складе: Невозможна поставка. Описание: Let $G$ be a reductive group over the field $F=k((t))$, where $k$ is an algebraic closure of a finite field, and let $W$ be the (extended) affine Weyl group of $G$. The associated affine Deligne-Lusztig varieties $X_x(b)$, which are indexed by elements $b \in G(F)$ and $x \in W$, were introduced by Rapoport. Basic questions about the varieties $X_x(b)$ which have remained largely open include when they are nonempty, and if nonempty, their dimension. The authors use techniques inspired by geometric group theory and combinatorial representation theory to address these questions in the case that $b$ is a pure translation, and so prove much of a sharpened version of a conjecture of Gortz, Haines, Kottwitz, and Reuman.The authors' approach is constructive and type-free, sheds new light on the reasons for existing results in the case that $b$ is basic, and reveals new patterns. Since they work only in the standard apartment of the building for $G(F)$, their results also hold in the $p$-adic context, where they formulate a definition of the dimension of a $p$-adic Deligne-Lusztig set. The authors present two immediate applications of their main results, to class polynomials of affine Hecke algebras and to affine reflection length.
Автор: Eduardo Garcia-Rio, Peter Gilkey, Stana Nik?evi?, Ramon Vazquez-Lorenzo Название: Applications of Affine and Weyl Geometry ISBN: 1608457591 ISBN-13(EAN): 9781608457595 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 46200.00 T Наличие на складе: Невозможна поставка. Описание: Pseudo-Riemannian geometry is, to a large extent, the study of the Levi-Civita connection, which is the unique torsion-free connection compatible with the metric structure. There are, however, other affine connections which arise in different contexts, such as conformal geometry, contact structures, Weyl structures, and almost Hermitian geometry. In this book, we reverse this point of view and instead associate an auxiliary pseudo-Riemannian structure of neutral signature to certain affine connections and use this correspondence to study both geometries. We examine Walker structures, Riemannian extensions, and Kähler--Weyl geometry from this viewpoint. This book is intended to be accessible to mathematicians who are not expert in the subject and to students with a basic grounding in differential geometry. Consequently, the first chapter contains a comprehensive introduction to the basic results and definitions we shall need-proofs are included of many of these results to make it as self-contained as possible. Para-complex geometry plays an important role throughout the book and consequently is treated carefully in various chapters, as is the representation theory underlying various results. It is a feature of this book that, rather than as regarding para-complex geometry as an adjunct to complex geometry, instead, we shall often introduce the para-complex concepts first and only later pass to the complex setting.The second and third chapters are devoted to the study of various kinds of Riemannian extensions that associate to an affine structure on a manifold a corresponding metric of neutral signature on its cotangent bundle. These play a role in various questions involving the spectral geometry of the curvature operator and homogeneous connections on surfaces. The fourth chapter deals with Kähler--Weyl geometry, which lies, in a certain sense, midway between affine geometry and Kähler geometry. Another feature of the book is that we have tried wherever possible to find the original references in the subject for possible historical interest. Thus, we have cited the seminal papers of Levi-Civita, Ricci, Schouten, and Weyl, to name but a few exemplars. We have also given different proofs of various results than those that are given in the literature, to take advantage of the unified treatment of the area given herein.
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