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Algebra - Abstract

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Inverse Galois Theory
by Malle, Gunter    Matzat, B. H.   
(Hardcover - English - 9783540628903)
Inverse Galois Theory is concerned with the question of which finite groups occur as Galois Groups over a given field. In particular, this includes the question of the structure and the representations of the absolute Galois group of K and also the question about its finite epimorphic images, the so-called inverse problem of Galois theory. In all these areas important progress was made in the last few years. The aim of the book is to give a consistent and reasonably complete survey of these results, with the main emphasis on the rigidity method and its applications. Among others the monograph presents the most successful known existence theorems and constructio ..
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Complex Semisimple Lie Algebras
by Jones, Glen    Serre, Jean-Pierre   
(Hardcover - English - 9783540678274)
These notes are a record of a course given in Algiers from 10th to 21st May, 1965. Their contents are as follows. The first two chapters are a summary, without proofs, of the general properties of nilpotent, solvable, and semisimple Lie algebras. These are well-known results, for which the reader can refer to, for example, Chapterof Bourbaki or my Harvard notes. The theory of complex semisimple algebras occupies Chapters III and IV. The proofs of the main theorems are essentially complete; however,have also found it useful to mention some complementary results without proof. These are indicated by an asterisk, and the proofs can be found in Bourbaki, Groupes et ..
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Clifford Algebras and Lie Theory
by Meinrenken, Eckhard       
(Hardcover - English - 9783642362156)
This monograph provides an introduction to the theory of Clifford algebras, with an emphasis on its connections with the theory of Lie groups and Lie algebras. The book starts with a detailed presentation of the main results on symmetric bilinear forms and Clifford algebras. It develops the spin groups and the spin representation, culminating in Cartan's famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes a presentation of Petracci's proof of the Poincaré-Birkhoff-Witt theorem. This is followed by discussions of Weil algebras, Chern--Weil theory, the quantum Weil algebra, and the cubic Dirac operator. The applicatio ..
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Lie Groups and Algebraic Groups
by Onishchik, Arkadij L.    Leites, Dimitry A.    Vinberg, Ernest B.
(Paperback - English - 9783642743368)
Extraordinary book based on Moscow University hectographed notes from 1968. The book is substantially extended, with material developed through posing of problems and a wealth of examples. Several tables have never been published before, e.g. decomposition of representations into irreducible components. Especially interesting for physicists. ..
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Galois Theory of Linear Differential Equations
by Van Der Put, Marius    Singer, Michael F.   
(Paperback - English - 9783642629167)
From the reviews: "This is a great book, which will hopefully become a classic in the subject of differential Galois theory. [...] the specialist, as well as the novice, have long been missing an introductory book covering also specific and advanced research topics. This gap is filled by the volume under review, and more than satisfactorily." Mathematical Reviews ..
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Quantum Groups and Their Representations
by Klimyk, Anatoli    Schmüdgen, Konrad   
(Paperback - English - 9783642646010)
The invention of quantum groups is one of the outstanding achievements of mathematical physics and mathematics in the late twentieth century. The birth of the new theory and its rapid development are results of a strong interrelation between mathematics and physics. Quantu groups arose in the work of L.D. Faddeev and the Leningrad school on the inverse scattering method in order to solve integrable models. The algebra Uq(sh) appeared first in 1981 in a paper by P.P. Kulish and N.Yu. Reshetikhin on the study of integrable XYZ models with highest spin. Its Hopf algebra structure was discovered later by E.K. Sklyanin. A major event was the discovery by V.G. Drinfel ..
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Approximation Theory in Tensor Product Spaces
by Light, William a.    Cheney, Elliot W.   
(Paperback - English - 9783540160571)
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Commutative Algebra: Expository Papers Dedicated to David Eisenbud on the Occasion of His 65th Birthday
by Peeva, Irena       
(Hardcover - English - 9781461452911)
Marian Aprodu: Lazarfeld-Mukai bundles and applications to syzygies.- Paul Aspinwall: Some Applications of Commutative Algebra to String Theory.- Angelica Benito, Eleonore Faber, and Karen Smith: Measuring singularities with Frobenius: the basics.- Christine Berkesch, Daniel Erman, and Manoj Kumini: Three avors of extremal Betti tables.- Manuel Blickle and Karl Schwede: p1 linear maps in algebra and geometry.- Markus Brodmann, Cao Luy Linh, and Maria-Helena Seiler: Castelnuovo-Mumford Regularity of Annihilators, Ext-Modules and Tor-Modules.- David Buchsbaum: Selections From the Letter-Place Panoply.- Aldo Conca, Emanuella DeNegri, and Maria-Evelina Rossi: Bounds ..
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Dynamical Systems of Algebraic Origin
by Schmidt, Klaus       
(Paperback - English - 9783034802765)
Although much of classical ergodic theory is concerned with single transformations and one-parameter flows, the subject inherits from statistical mechanics not only its name, but also an obligation to analyze spatially extended systems with multidimensional symmetry groups. However, the wealth of concrete and natural examples which has contributed so much to the appeal and development of classical dynamics, is noticeably absent in this more general theory. The purpose of this book is to help remedy this scarcity of explicit examples by introducing​ a class of continuous Zd-actions diverse enough to exhibit many of the new phenomena encountered in the trans ..
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Topics in Noncommutative Algebra: The Theorem of Campbell, Baker, Hausdorff and Dynkin
by Bonfiglioli, Andrea    Fulci, Roberta   
(Paperback - English - 9783642225963)
Motivated by the importance of the Campbell, Baker, Hausdorff, Dynkin Theorem in many different branches of Mathematics and Physics (Lie group-Lie algebra theory, linear PDEs, Quantum and Statistical Mechanics, Numerical Analysis, Theoretical Physics, Control Theory, sub-Riemannian Geometry), this monograph is intended to: fully enable readers (graduates or specialists, mathematicians, physicists or applied scientists, acquainted with Algebra or not) to understand and apply the statements and numerous corollaries of the main result, provide a wide spectrum of proofs from the modern literature, comparing different techniques and furnishing a unifying point of vie ..
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Commutative Algebra: Chapters 1-7
by Bourbaki, N.       
(Paperback - English - 9783540642398)
This is the softcover reprint of the English translation of 1972 (available from Springer since 1989) of the first 7 chapters of Bourbaki's 'Alg bre commutative'. It provides a very complete treatment of commutative algebra, enabling the reader to go further and study algebraic or arithmetic geometry. The first 3 chapters treat in succession the concepts of flatness, localization and completions (in the general setting of graduations and filtrations). Chapter 4 studies associated prime ideals and the primary decomposition. Chapter 5 deals with integers, integral closures and finitely generated algebras over a field (including the Nullstellensatz). Chapter 6 stud ..
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Noncommutative Iwasawa Main Conjectures Over Totally Real Fields: Münster, April 2011
by Coates, John    Schneider, Peter    Sujatha, R.
(Hardcover - English - 9783642321986)
The algebraic techniques developed by Kakde will almost certainly lead eventually to major progress in the study of congruences between automorphic forms and the main conjectures of non-commutative Iwasawa theory for many motives. Non-commutative Iwasawa theory has emerged dramatically over the last decade, culminating in the recent proof of the non-commutative main conjecture for the Tate motive over a totally real p-adic Lie extension of a number field, independently by Ritter and Weiss on the one hand, and Kakde on the other. The initial ideas for giving a precise formulation of the non-commutative main conjecture were discovered by Venjakob, and were then sy ..
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Galois Theory, Coverings, and Riemann Surfaces
by Khovanskii, Askold    Timorin, Vladlen    Kiritchenko, Valentina
(Hardcover - English - 9783642388408)
Chapter 1 Galois Theory: 1.1 Action of a Solvable Group and Representability by Radicals.- 1.2 Fixed Points under an Action of a Finite Group and Its Subgroups.- 1.3 Field Automorphisms and Relations between Elements in a Field.- 1.4 Action of a k -Solvable Group and Representability by k -Radicals.- 1.5 Galois Equations.- 1.6 Automorphisms Connected with a Galois Equation.- 1.7 The Fundamental Theorem of Galois Theory.- 1.8 A Criterion for Solvability of Equations by Radicals.- 1.9 A Criterion for Solvability of Equations by k -Radicals.- 1.10 Unsolvability of Complicated Equations by Solving Simpler Equations.- 1.11 Finite Fields.- Chapter 2 Coverings: 2.1 Cov ..
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The Linear Algebra a Beginning Graduate Student Ought to Know
by Golan, Jonathan S.       
(Paperback - English - 9789400726352)
Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as to computer science, to the physical, biological, and social sciences, and to engineering. It encompasses an extensive corpus of theoretical results as well as a large and rapidly-growing body of computational techniques. Unfortunately, in the past decade, the content of linear algebra courses required to complete an undergraduate degree in mathematics has been depleted to the extent that they fail to provide a sufficient theoretical or computational background. Students are not only less able to formulate or even ..
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Symmetry Orbits
by Verheyen, Hugo F.       
(Paperback - English - 9781461286394)
In a broad sense design science is the grammar of a language of images rather than of words. Modem communication techniques enable us to transmit and reconstitute images without needing to know a specific verbal sequence language such as the Morse code or Hungarian. Inter- national traffic signs use international image symbols which are not An image language differs specific to any particular verbal language. from a verbal one in that the latter uses a linear string of symbols, whereas the former is multidimensional. Architectural renderings commonly show projections onto three mutually perpendicular planes, or consist of cross sections at different altitudes ca ..
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Operator Algebra and Dynamics: Nordforsk Network Closing Conference, Faroe Islands, May 2012
by Carlsen, Toke M.    Eilers, Søren    Restorff, Gunnar
(Hardcover - English - 9783642394584)
Based on presentations given at the NordForsk Network Closing Conference "Operator Algebra and Dynamics," held in Gjáargarður, Faroe Islands, in May 2012, this book features high quality research contributions and review articles by researchers associated with the NordForsk network and leading experts that explore the fundamental role of operator algebras and dynamical systems in mathematics with possible applications to physics, engineering and computer science. It covers the following topics: von Neumann algebras arising from discrete measured groupoids, purely infinite Cuntz-Krieger algebras, filtered K-theory over finite topological spaces, C* -algebras as ..
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Elements of the Representation Theory of the Jacobi Group
by Berndt, Rolf    Schmidt, Ralf   
(Paperback - English - 9783034802826)
After Pyatetski-Shapiro PS1] and Satake Sa1] introduced, independent of one another, an early form of the Jacobi Theory in 1969 (while not naming it as such), this theory was given a de?nite push by the book The Theory of Jacobi Forms by Eichler and Zagier in 1985. Now, there are some overview articles describing the developments in the theory of the Jacobigroupandits autom- phic forms, for instance by Skoruppa Sk2], Berndt Be5] and Kohnen Ko]. We refertotheseformorehistoricaldetailsandmanymorenamesofauthorsactive inthistheory, whichstretchesnowfromnumbertheoryandalgebraicgeometry to theoretical physics. But let us only brie?y indicate several- sometimes very ..
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Real Quaternionic Calculus Handbook
by Morais, João Pedro    Georgiev, Svetlin    Sprößig, Wolfgang
(Paperback - English - 9783034806213)
1 An introduction to quaternions.- 2 Quaternions and spatial rotation.- 3 Quaternion sequences.- 4 Quaternion series and infinite products.- 5 Exponents and logarithms.- 6 Trigonometric functions.- 7 Hyperbolic functions.- 8 Inverse hyperbolic and trigonometric functions.- 9 Quaternion matrices.- 10 Monomials, polynomials and binomials.- 11 Solutions.- Bibliography.- Index. ..
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Dynamics of Foliations, Groups and Pseudogroups
by Walczak, Pawel       
(Paperback - English - 9783034896115)
This book deals with the dynamics of general systems such as foliations, groups and pseudogroups, systems which are closely related via the notion of holonomy. Since dynamics'' is a very extensive term, we focus on some of its aspects only. Roughly speaking, we concentrate on notions and results related to different ways of measuring complexity of the systems under consideration. More precisely, we deal with different types of growth, entropies and dimensions of limiting objects. Throughout the book, the reader will find a good number of inspirating problems related to the topics covered. ..
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Discrete Groups, Expanding Graphs and Invariant Measures
by Rogawski, Jonathan D.    Lubotzky, Alex   
(Paperback - English - 9783034603317)
In the last ?fteen years two seemingly unrelated problems, one in computer science and the other in measure theory, were solved by amazingly similar techniques from representation theory and from analytic number theory. One problem is the - plicit construction of expanding graphs ( expanders ). These are highly connected sparse graphs whose existence can be easily demonstrated but whose explicit c- struction turns out to be a dif?cult task. Since expanders serve as basic building blocks for various distributed networks, an explicit construction is highly des- able. The other problem is one posed by Ruziewicz about seventy years ago and studied by Banach [Ba]. It ..
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