Affine Sets And Affine Groups

Author : D. G. Northcott
Publisher : Cambridge University Press
ISBN 13 : 052122909X
Total Pages : 297 pages
Book Rating : 4.98/5 ( download)

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Download or read book Affine Sets and Affine Groups written by D. G. Northcott and published by Cambridge University Press. This book was released on 1980-05-08 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: In these notes, first published in 1980, Professor Northcott provides a self-contained introduction to the theory of affine algebraic groups for mathematicians with a basic knowledge of communicative algebra and field theory. The book divides into two parts. The first four chapters contain all the geometry needed for the second half of the book which deals with affine groups. Alternatively the first part provides a sure introduction to the foundations of algebraic geometry. Any affine group has an associated Lie algebra. In the last two chapters, the author studies these algebras and shows how, in certain important cases, their properties can be transferred back to the groups from which they arose. These notes provide a clear and carefully written introduction to algebraic geometry and algebraic groups.

Author : Douglas Geoffrey Northcott
Publisher :
ISBN 13 : 9781107087170
Total Pages : 285 pages
Book Rating : 4.71/5 ( download)

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Download or read book Affine Sets and Affine Groups written by Douglas Geoffrey Northcott and published by . This book was released on 1980 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to the theory of affine algebraic groups for mathematicians with a basic knowledge of communicative algebra and field theory.

Author : W.C. Waterhouse
Publisher : Springer Science & Business Media
ISBN 13 : 1461262178
Total Pages : 167 pages
Book Rating : 4.76/5 ( download)

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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 : Ernst Snapper
Publisher : Elsevier
ISBN 13 : 1483269337
Total Pages : 456 pages
Book Rating : 4.37/5 ( download)

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Download or read book Metric Affine Geometry written by Ernst Snapper and published by Elsevier. This book was released on 2014-05-10 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Metric Affine Geometry focuses on linear algebra, which is the source for the axiom systems of all affine and projective geometries, both metric and nonmetric. This book is organized into three chapters. Chapter 1 discusses nonmetric affine geometry, while Chapter 2 reviews inner products of vector spaces. The metric affine geometry is treated in Chapter 3. This text specifically discusses the concrete model for affine space, dilations in terms of coordinates, parallelograms, and theorem of Desargues. The inner products in terms of coordinates and similarities of affine spaces are also elaborated. The prerequisites for this publication are a course in linear algebra and an elementary course in modern algebra that includes the concepts of group, normal subgroup, and quotient group. This monograph is suitable for students and aspiring geometry high school teachers.

Author : K. T. Arasu
Publisher : Walter de Gruyter
ISBN 13 : 9783110147919
Total Pages : 480 pages
Book Rating : 4.12/5 ( download)

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Download or read book Groups, Difference Sets, and the Monster written by K. T. Arasu and published by Walter de Gruyter. This book was released on 1996 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Groups, Difference Sets, and the Monster".

Author : Thierry Vialar
Publisher : BoD - Books on Demand
ISBN 13 : 2955199001
Total Pages : 1134 pages
Book Rating : 4.08/5 ( download)

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Download or read book Handbook of Mathematics written by Thierry Vialar and published by BoD - Books on Demand. This book was released on 2016-12-07 with total page 1134 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book consists of XI Parts and 28 Chapters covering all areas of mathematics. It is a tool for students, scientists, engineers, students of many disciplines, teachers, professionals, writers and also for a general reader with an interest in mathematics and in science. It provides a wide range of mathematical concepts, definitions, propositions, theorems, proofs, examples, and numerous illustrations. The difficulty level can vary depending on chapters, and sustained attention will be required for some. The structure and list of Parts are quite classical: I. Foundations of Mathematics, II. Algebra, III. Number Theory, IV. Geometry, V. Analytic Geometry, VI. Topology, VII .Algebraic Topology, VIII. Analysis, IX. Category Theory, X. Probability and Statistics, XI. Applied Mathematics. Appendices provide useful lists of symbols and tables for ready reference. The publisher’s hope is that this book, slightly revised and in a convenient format, will serve the needs of readers, be it for study, teaching, exploration, work, or research.

Author : Roger William Carter
Publisher : Cambridge University Press
ISBN 13 : 9780521851381
Total Pages : 662 pages
Book Rating : 4.86/5 ( download)

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Download or read book Lie Algebras of Finite and Affine Type written by Roger William Carter and published by Cambridge University Press. This book was released on 2005-10-27 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough but relaxed mathematical treatment of Lie algebras.

Author : P. M. Neumann
Publisher : Oxford University Press, USA
ISBN 13 : 9780198534518
Total Pages : 268 pages
Book Rating : 4.15/5 ( download)

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Download or read book Groups and Geometry written by P. M. Neumann and published by Oxford University Press, USA. This book was released on 1994 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the Oxford Mathematical Institute notes for undergraduate and first-year postgraduates. The first half of the book covers groups, the second half covers geometry and both parts contain a number of exercises.

Author : Manfred Bernd Wischnewsky
Publisher :
ISBN 13 :
Total Pages : 52 pages
Book Rating : 4.87/5 ( download)

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Download or read book On Linear Representations of Affine Groups written by Manfred Bernd Wischnewsky and published by . This book was released on 1975 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : William C. Waterhouse
Publisher :
ISBN 13 : 9787506200967
Total Pages : 164 pages
Book Rating : 4.61/5 ( download)

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Download or read book Introduction to Affine Group Schemes written by William C. Waterhouse and published by . This book was released on 1979 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: