Affine Sets And Affine Groups PDF Download
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Author | : D. G. Northcott |
Publisher | : Cambridge University Press |
Total Pages | : 297 |
Release | : 1980-05-08 |
Genre | : Mathematics |
ISBN | : 052122909X |
Download Affine Sets and Affine Groups Book in PDF, ePub and Kindle
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 | : |
Total Pages | : 285 |
Release | : 1980 |
Genre | : Geometry, Affine |
ISBN | : 9781107087170 |
Download Affine Sets and Affine Groups Book in PDF, ePub and Kindle
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 |
Total Pages | : 167 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461262178 |
Download Introduction to Affine Group Schemes Book in PDF, ePub and Kindle
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 | : D. G. Northcott |
Publisher | : |
Total Pages | : |
Release | : 1980 |
Genre | : |
ISBN | : |
Download Aftine Sets and Affine Groups Book in PDF, ePub and Kindle
Author | : Manfred Bernd Wischnewsky |
Publisher | : |
Total Pages | : 50 |
Release | : 1975 |
Genre | : Categories (Mathematics) |
ISBN | : |
Download On Linear Representations of Affine Groups Book in PDF, ePub and Kindle
Author | : William C. Waterhouse |
Publisher | : |
Total Pages | : 164 |
Release | : 1979 |
Genre | : Group schemes (Mathematics). |
ISBN | : 9787506200967 |
Download Introduction to Affine Group Schemes Book in PDF, ePub and Kindle
Author | : Changchun Li |
Publisher | : |
Total Pages | : 264 |
Release | : 1994 |
Genre | : |
ISBN | : |
Download Affine Group Schemes and P-formal Group Schemes Book in PDF, ePub and Kindle
Author | : Ernst Snapper |
Publisher | : Elsevier |
Total Pages | : 456 |
Release | : 2014-05-10 |
Genre | : Mathematics |
ISBN | : 1483269337 |
Download Metric Affine Geometry Book in PDF, ePub and Kindle
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 | : Manfred Bernd Wischnewsky |
Publisher | : |
Total Pages | : |
Release | : 1975 |
Genre | : |
ISBN | : |
Download On linear representation of affine groups Book in PDF, ePub and Kindle
Author | : Roger William Carter |
Publisher | : Cambridge University Press |
Total Pages | : 662 |
Release | : 2005-10-27 |
Genre | : Mathematics |
ISBN | : 9780521851381 |
Download Lie Algebras of Finite and Affine Type Book in PDF, ePub and Kindle
This book provides a thorough but relaxed mathematical treatment of Lie algebras.