Download or read book Linear Groups written by Martyn R. Dixon and published by CRC Press. This book was released on 2020-04-03 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Groups: The Accent on Infinite Dimensionality explores some of the main results and ideas in the study of infinite-dimensional linear groups. The theory of finite dimensional linear groups is one of the best developed algebraic theories. The array of articles devoted to this topic is enormous, and there are many monographs concerned with matrix groups, ranging from old, classical texts to ones published more recently. However, in the case when the dimension is infinite (and such cases arise quite often), the reality is quite different. The situation with the study of infinite dimensional linear groups is like the situation that has developed in the theory of groups, in the transition from the study of finite groups to the study of infinite groups which appeared about one hundred years ago. It is well known that this transition was extremely efficient and led to the development of a rich and central branch of algebra: Infinite group theory. The hope is that this book can be part of a similar transition in the field of linear groups. Features This is the first book dedicated to infinite-dimensional linear groups This is written for experts and graduate students specializing in algebra and parallel disciplines This book discusses a very new theory and accumulates many important and useful results

Download or read book Infinite Linear Groups written by Bertram Wehrfritz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: By a linear group we mean essentially a group of invertible matrices with entries in some commutative field. A phenomenon of the last twenty years or so has been the increasing use of properties of infinite linear groups in the theory of (abstract) groups, although the story of infinite linear groups as such goes back to the early years of this century with the work of Burnside and Schur particularly. Infinite linear groups arise in group theory in a number of contexts. One of the most common is via the automorphism groups of certain types of abelian groups, such as free abelian groups of finite rank, torsion-free abelian groups of finite rank and divisible abelian p-groups of finite rank. Following pioneering work of Mal'cev many authors have studied soluble groups satisfying various rank restrictions and their automor phism groups in this way, and properties of infinite linear groups now play the central role in the theory of these groups. It has recently been realized that the automorphism groups of certain finitely generated soluble (in particular finitely generated metabelian) groups contain significant factors isomorphic to groups of automorphisms of finitely generated modules over certain commutative Noetherian rings. The results of our Chapter 13, which studies such groups of automorphisms, can be used to give much information here.

Download or read book Lie Groups written by Wulf Rossmann and published by Oxford University Press, USA. This book was released on 2006 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of Lie groups and their representations at the advanced undergraduate or beginning graduate level. It covers the essentials of the subject starting from basic undergraduate mathematics. The correspondence between linear Lie groups and Lie algebras is developed in its local and global aspects. The classical groups are analyzed in detail, first with elementary matrix methods, then with the help of the structural tools typical of the theory of semisimple groups, such as Cartan subgroups, root, weights and reflections. The fundamental groups of the classical groups are worked out as an application of these methods. Manifolds are introduced when needed, in connection with homogeneous spaces, and the elements of differential and integral calculus on manifolds are presented, with special emphasis on integration on groups and homogeneous spaces. Representation theory starts from first principles, such as Schur's lemma and its consequences, and proceeds from there to the Peter-Weyl theorem, Weyl's character formula, and the Borel-Weil theorem, all in the context of linear groups.

Download or read book Linear Algebraic Groups written by James E. Humphreys and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: James E. Humphreys is a distinguished Professor of Mathematics at the University of Massachusetts at Amherst. He has previously held posts at the University of Oregon and New York University. His main research interests include group theory and Lie algebras, and this graduate level text is an exceptionally well-written introduction to everything about linear algebraic groups.

Download or read book Linear Representations of Finite Groups written by Jean Pierre Serre and published by . This book was released on 1996 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Linear Algebraic Groups written by T.A. Springer and published by Springer Science & Business Media. This book was released on 2010-10-12 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this book presented the theory of linear algebraic groups over an algebraically closed field. The second edition, thoroughly revised and expanded, extends the theory over arbitrary fields, which are not necessarily algebraically closed. It thus represents a higher aim. As in the first edition, the book includes a self-contained treatment of the prerequisites from algebraic geometry and commutative algebra, as well as basic results on reductive groups. As a result, the first part of the book can well serve as a text for an introductory graduate course on linear algebraic groups.

Download or read book Linear Algebraic Groups written by Armand Borel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised, enlarged edition of Linear Algebraic Groups (1969) starts by presenting foundational material on algebraic groups, Lie algebras, transformation spaces, and quotient spaces. It then turns to solvable groups, general properties of linear algebraic groups, and Chevally’s structure theory of reductive groups over algebraically closed groundfields. It closes with a focus on rationality questions over non-algebraically closed fields.

Download or read book Linear Algebraic Groups and Finite Groups of Lie Type written by Gunter Malle and published by Cambridge University Press. This book was released on 2011-09-08 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originating from a summer school taught by the authors, this concise treatment includes many of the main results in the area. An introductory chapter describes the fundamental results on linear algebraic groups, culminating in the classification of semisimple groups. The second chapter introduces more specialized topics in the subgroup structure of semisimple groups and describes the classification of the maximal subgroups of the simple algebraic groups. The authors then systematically develop the subgroup structure of finite groups of Lie type as a consequence of the structural results on algebraic groups. This approach will help students to understand the relationship between these two classes of groups. The book covers many topics that are central to the subject, but missing from existing textbooks. The authors provide numerous instructive exercises and examples for those who are learning the subject as well as more advanced topics for research students working in related areas.

Download or read book Linear Representations of Groups written by E.B. Vinberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an exposition of the fundamentals of the theory of linear representations of finite and compact groups, as well as elements of the the ory of linear representations of Lie groups. As an application we derive the Laplace spherical functions. The book is based on lectures that I delivered in the framework of the experimental program at the Mathematics-Mechanics Faculty of Moscow State University and at the Faculty of Professional Skill Improvement. My aim has been to give as simple and detailed an account as possible of the problems considered. The book therefore makes no claim to completeness. Also, it can in no way give a representative picture of the modern state of the field under study as does, for example, the monograph of A. A. Kirillov [3]. For a more complete acquaintance with the theory of representations of finite groups we recommend the book of C. W. Curtis and I. Reiner [2], and for the theory of representations of Lie groups, that of M. A. Naimark [6]. Introduction The theory of linear representations of groups is one of the most widely ap plied branches of algebra. Practically every time that groups are encountered, their linear representations play an important role. In the theory of groups itself, linear representations are an irreplaceable source of examples and a tool for investigating groups. In the introduction we discuss some examples and en route we introduce a number of notions of representation theory. O.

Download or read book Algebra IV written by A.I. Kostrikin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group theory is one of the most fundamental branches of mathematics. This highly accessible volume of the Encyclopaedia is devoted to two important subjects within this theory. Extremely useful to all mathematicians, physicists and other scientists, including graduate students who use group theory in their work.

Download or read book Linear Groups with an Exposition of Galois Field Theory written by Leonard Eugene Dickson and published by Cosimo, Inc.. This book was released on 2007-04-01 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic in the field of abstract algebra has been called "the first systematic treatment of finite fields in the mathematical literature." Divided into two sections-"Introduction to the Galois Field Theory" and "Theory of Linear Groups in a Galois Field"-and crammed with examples and theorems, Linear Groups remains relevant more than a century after its publication. Learn about: . definition and properties of finite fields . classification and determination of irreducible quantics . miscellaneous properties of Galois Fields . analytic representation of substitutions on the marks of a Galois Field . the Abelian linear group . the hyperabelian group . the hyperorthogonal and related linear groups . and much more. This historic contribution to the theory of groups is still appreciated by mathematicians today. American mathematician LEONARD EUGENE DICKSON (1874-1954) received the University of Chicago's first doctorate in mathematics, and later taught there for 39 years. His published works include Linear Algebras (1914), History of the Theory of Numbers (1919-23), and Studies in the Theory of Numbers (1930).

Download or read book Linear Groups written by Martyn R. Dixon and published by CRC Press. This book was released on 2020-04-03 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Groups: The Accent on Infinite Dimensionality explores some of the main results and ideas in the study of infinite-dimensional linear groups. The theory of finite dimensional linear groups is one of the best developed algebraic theories. The array of articles devoted to this topic is enormous, and there are many monographs concerned with matrix groups, ranging from old, classical texts to ones published more recently. However, in the case when the dimension is infinite (and such cases arise quite often), the reality is quite different. The situation with the study of infinite dimensional linear groups is like the situation that has developed in the theory of groups, in the transition from the study of finite groups to the study of infinite groups which appeared about one hundred years ago. It is well known that this transition was extremely efficient and led to the development of a rich and central branch of algebra: Infinite group theory. The hope is that this book can be part of a similar transition in the field of linear groups. Features This is the first book dedicated to infinite-dimensional linear groups This is written for experts and graduate students specializing in algebra and parallel disciplines This book discusses a very new theory and accumulates many important and useful results

Download or read book Linear Algebraic Groups and Their Representations written by Richard S. Elman and published by American Mathematical Soc.. This book was released on 1993 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Brings together a wide variety of themes under a single unifying perspective The proceedings of a conference on Linear algebraic Groups and their Representations - the text gets to grips with the fundamental nature of this subject and its interaction with a wide variety of active areas in mathematics and physics.

Download or read book Groups Matrices and Vector Spaces written by James B. Carrell and published by Springer. This book was released on 2017-09-02 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group. Applications involving symm etry groups, determinants, linear coding theory and cryptography are interwoven throughout. Each section ends with ample practice problems assisting the reader to better understand the material. Some of the applications are illustrated in the chapter appendices. The author's unique melding of topics evolved from a two semester course that he taught at the University of British Columbia consisting of an undergraduate honors course on abstract linear algebra and a similar course on the theory of groups. The combined content from both makes this rare text ideal for a year-long course, covering more material than most linear algebra texts. It is also optimal for independent study and as a supplementary text for various professional applications. Advanced undergraduate or graduate students in mathematics, physics, computer science and engineering will find this book both useful and enjoyable.

Download or read book Computation with Linear Algebraic Groups written by Willem Adriaan de Graaf and published by CRC Press. This book was released on 2017-08-07 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed as a self-contained account of a number of key algorithmic problems and their solutions for linear algebraic groups, this book combines in one single text both an introduction to the basic theory of linear algebraic groups and a substantial collection of useful algorithms. Computation with Linear Algebraic Groups offers an invaluable guide to graduate students and researchers working in algebraic groups, computational algebraic geometry, and computational group theory, as well as those looking for a concise introduction to the theory of linear algebraic groups.

Download or read book Diophantine Approximation on Linear Algebraic Groups written by Michel Waldschmidt and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function ez: a central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. Two chapters provide complete and simplified proofs of zero estimates (due to Philippon) on linear algebraic groups.

Download or read book Linear and Projective Representations of Symmetric Groups written by Alexander Kleshchev and published by Cambridge University Press. This book was released on 2005-06-30 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: The representation theory of symmetric groups is one of the most beautiful, popular and important parts of algebra, with many deep relations to other areas of mathematics. Kleshchev describes a new approach to the subject, based on the recent work of Lascoux, Leclerc, Thibon, Ariki, Grojnowski and Brundan, as well as his own