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Author :
Publisher : Elsevier
ISBN 13 : 008087150X
Total Pages : 373 pages
Book Rating : 4.0/5 (88 download)
Download or read book Introduction to Algebraic Geometry and Algebraic Groups written by and published by Elsevier. This book was released on 1980-01-01 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Algebraic Geometry and Algebraic Groups
Author : Meinolf Geck
Publisher : Oxford University Press
ISBN 13 : 019967616X
Total Pages : 321 pages
Book Rating : 4.1/5 (996 download)
Download or read book An Introduction to Algebraic Geometry and Algebraic Groups written by Meinolf Geck and published by Oxford University Press. This book was released on 2013-03-14 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible text introducing algebraic groups at advanced undergraduate and early graduate level, this book covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields.
Author : Serge Lang
Publisher : Courier Dover Publications
ISBN 13 : 048683980X
Total Pages : 273 pages
Book Rating : 4.4/5 (868 download)
Download or read book Introduction to Algebraic Geometry written by Serge Lang and published by Courier Dover Publications. This book was released on 2019-03-20 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Author Serge Lang defines algebraic geometry as the study of systems of algebraic equations in several variables and of the structure that one can give to the solutions of such equations. The study can be carried out in four ways: analytical, topological, algebraico-geometric, and arithmetic. This volume offers a rapid, concise, and self-contained introductory approach to the algebraic aspects of the third method, the algebraico-geometric. The treatment assumes only familiarity with elementary algebra up to the level of Galois theory. Starting with an opening chapter on the general theory of places, the author advances to examinations of algebraic varieties, the absolute theory of varieties, and products, projections, and correspondences. Subsequent chapters explore normal varieties, divisors and linear systems, differential forms, the theory of simple points, and algebraic groups, concluding with a focus on the Riemann-Roch theorem. All the theorems of a general nature related to the foundations of the theory of algebraic groups are featured.
Author : J. S. Milne
Publisher : Cambridge University Press
ISBN 13 : 1107167485
Total Pages : 665 pages
Book Rating : 4.1/5 (71 download)
Download or read book Algebraic Groups written by J. S. Milne and published by Cambridge University Press. This book was released on 2017-09-21 with total page 665 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.
Author : Pavel I. Etingof
Publisher : American Mathematical Soc.
ISBN 13 : 0821853511
Total Pages : 240 pages
Book Rating : 4.8/5 (218 download)
Download or read book Introduction to Representation Theory written by Pavel I. Etingof and published by American Mathematical Soc.. This book was released on 2011 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.
Author : James E. Humphreys
Publisher : Springer Science & Business Media
ISBN 13 : 1468494430
Total Pages : 259 pages
Book Rating : 4.4/5 (684 download)
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.
Author : T.A. Springer
Publisher : Springer Science & Business Media
ISBN 13 : 0817648402
Total Pages : 347 pages
Book Rating : 4.8/5 (176 download)
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.
Author : Jens Carsten Jantzen
Publisher : American Mathematical Soc.
ISBN 13 : 082184377X
Total Pages : 594 pages
Book Rating : 4.8/5 (218 download)
Download or read book Representations of Algebraic Groups written by Jens Carsten Jantzen and published by American Mathematical Soc.. This book was released on 2003 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.
Author : Patrice Tauvel
Publisher : Springer Science & Business Media
ISBN 13 : 3540274278
Total Pages : 650 pages
Book Rating : 4.5/5 (42 download)
Download or read book Lie Algebras and Algebraic Groups written by Patrice Tauvel and published by Springer Science & Business Media. This book was released on 2005-08-08 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: Devoted to the theory of Lie algebras and algebraic groups, this book includes a large amount of commutative algebra and algebraic geometry so as to make it as self-contained as possible. The aim of the book is to assemble in a single volume the algebraic aspects of the theory, so as to present the foundations of the theory in characteristic zero. Detailed proofs are included, and some recent results are discussed in the final chapters.
Author : Walter Ricardo Ferrer Santos
Publisher : CRC Press
ISBN 13 : 1482239167
Total Pages : 479 pages
Book Rating : 4.4/5 (822 download)
Download or read book Actions and Invariants of Algebraic Groups written by Walter Ricardo Ferrer Santos and published by CRC Press. This book was released on 2017-09-19 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: Actions and Invariants of Algebraic Groups, Second Edition presents a self-contained introduction to geometric invariant theory starting from the basic theory of affine algebraic groups and proceeding towards more sophisticated dimensions." Building on the first edition, this book provides an introduction to the theory by equipping the reader with the tools needed to read advanced research in the field. Beginning with commutative algebra, algebraic geometry and the theory of Lie algebras, the book develops the necessary background of affine algebraic groups over an algebraically closed field, and then moves toward the algebraic and geometric aspects of modern invariant theory and quotients.
Author : Robin Hartshorne
Publisher : Springer Science & Business Media
ISBN 13 : 1475738498
Total Pages : 511 pages
Book Rating : 4.4/5 (757 download)
Download or read book Algebraic Geometry written by Robin Hartshorne and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.
Author : Yuri V. Nesterenko
Publisher : Springer
ISBN 13 : 3540445501
Total Pages : 257 pages
Book Rating : 4.5/5 (44 download)
Download or read book Introduction to Algebraic Independence Theory written by Yuri V. Nesterenko and published by Springer. This book was released on 2003-07-01 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last five years there has been very significant progress in the development of transcendence theory. A new approach to the arithmetic properties of values of modular forms and theta-functions was found. The solution of the Mahler-Manin problem on values of modular function j(tau) and algebraic independence of numbers pi and e^(pi) are most impressive results of this breakthrough. The book presents these and other results on algebraic independence of numbers and further, a detailed exposition of methods created in last the 25 years, during which commutative algebra and algebraic geometry exerted strong catalytic influence on the development of the subject.
Author : Joe Harris
Publisher : Springer Science & Business Media
ISBN 13 : 1475721897
Total Pages : 344 pages
Book Rating : 4.4/5 (757 download)
Download or read book Algebraic Geometry written by Joe Harris and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book succeeds brilliantly by concentrating on a number of core topics...and by treating them in a hugely rich and varied way. The author ensures that the reader will learn a large amount of classical material and perhaps more importantly, will also learn that there is no one approach to the subject. The essence lies in the range and interplay of possible approaches. The author is to be congratulated on a work of deep and enthusiastic scholarship." --MATHEMATICAL REVIEWS
Author : T.A. Springer
Publisher : Birkhäuser
ISBN 13 : 9780817648541
Total Pages : 334 pages
Book Rating : 4.6/5 (485 download)
Download or read book Linear Algebraic Groups written by T.A. Springer and published by Birkhäuser. This book was released on 2014-01-29 with total page 334 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.
Author : W.C. Waterhouse
Publisher : Springer Science & Business Media
ISBN 13 : 1461262178
Total Pages : 167 pages
Book Rating : 4.4/5 (612 download)
Download or read book Introduction to Affine Group Schemes written by W.C. Waterhouse and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ah Love! Could you and I with Him consl?ire To grasp this sorry Scheme of things entIre' KHAYYAM People investigating algebraic groups have studied the same objects in many different guises. My first goal thus has been to take three different viewpoints and demonstrate how they offer complementary intuitive insight into the subject. In Part I we begin with a functorial idea, discussing some familiar processes for constructing groups. These turn out to be equivalent to the ring-theoretic objects called Hopf algebras, with which we can then con struct new examples. Study of their representations shows that they are closely related to groups of matrices, and closed sets in matrix space give us a geometric picture of some of the objects involved. This interplay of methods continues as we turn to specific results. In Part II, a geometric idea (connectedness) and one from classical matrix theory (Jordan decomposition) blend with the study of separable algebras. In Part III, a notion of differential prompted by the theory of Lie groups is used to prove the absence of nilpotents in certain Hopf algebras. The ring-theoretic work on faithful flatness in Part IV turns out to give the true explanation for the behavior of quotient group functors. Finally, the material is connected with other parts of algebra in Part V, which shows how twisted forms of any algebraic structure are governed by its automorphism group scheme.
Author : Arkadij L. Onishchik
Publisher : Springer Science & Business Media
ISBN 13 : 364274334X
Total Pages : 347 pages
Book Rating : 4.6/5 (427 download)
Download or read book Lie Groups and Algebraic Groups written by Arkadij L. Onishchik and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the notes of the authors' seminar on algebraic and Lie groups held at the Department of Mechanics and Mathematics of Moscow University in 1967/68. Our guiding idea was to present in the most economic way the theory of semisimple Lie groups on the basis of the theory of algebraic groups. Our main sources were A. Borel's paper [34], C. ChevalIey's seminar [14], seminar "Sophus Lie" [15] and monographs by C. Chevalley [4], N. Jacobson [9] and J-P. Serre [16, 17]. In preparing this book we have completely rearranged these notes and added two new chapters: "Lie groups" and "Real semisimple Lie groups". Several traditional topics of Lie algebra theory, however, are left entirely disregarded, e.g. universal enveloping algebras, characters of linear representations and (co)homology of Lie algebras. A distinctive feature of this book is that almost all the material is presented as a sequence of problems, as it had been in the first draft of the seminar's notes. We believe that solving these problems may help the reader to feel the seminar's atmosphere and master the theory. Nevertheless, all the non-trivial ideas, and sometimes solutions, are contained in hints given at the end of each section. The proofs of certain theorems, which we consider more difficult, are given directly in the main text. The book also contains exercises, the majority of which are an essential complement to the main contents.
Author : Tonny Albert Springer
Publisher : Springer Science & Business Media
ISBN 13 : 0817640215
Total Pages : 353 pages
Book Rating : 4.8/5 (176 download)
Download or read book Linear Algebraic Groups written by Tonny Albert Springer and published by Springer Science & Business Media. This book was released on 1998 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: "[The first] ten chapters...are an efficient, accessible, and self-contained introduction to affine algebraic groups over an algebraically closed field. The author includes exercises and the book is certainly usable by graduate students as a text or for self-study...the author [has a] student-friendly style⦠[The following] seven chapters... would also be a good introduction to rationality issues for algebraic groups. A number of results from the literatureâ¦appear for the first time in a text." âMathematical Reviews(Review of the Second Edition) "This book is a completely new version of the first edition. The aim of the old book was to present the theory of linear algebraic groups over an algebraically closed field. Reading that book, many people entered the research field of linear algebraic groups. The present book has a wider scope. Its aim is to treat the theory of linear algebraic groups over arbitrary fields. Again, the author keeps the treatment of prerequisites self-contained. The material of the first ten chapters covers the contents of the old book, but the arrangement is somewhat different and there are additions, such as the basic facts about algebraic varieties and algebraic groups over a ground field, as well as an elementary treatment of Tannaka's theorem. These chapters can serve as a text for an introductory course on linear algebraic groups. The last seven chapters are new. They deal with algebraic groups over arbitrary fields. Some of the material has not been dealt with before in other texts, such as Rosenlicht's results about solvable groups in Chapter 14, the theorem of Borel and Tits on the conjugacy over the ground field of maximal split tori in an arbitrary linear algebraic group in Chapter 15, and the Tits classification of simple groups over a ground field in Chapter 17. The book includes many exercises and a subject index." âZentralblatt Math(Review of the Second Edition)
