Jordan Algebras and Algebraic Groups

Jordan Algebras and Algebraic Groups
Author: Tonny A. Springer
Publisher: Springer Science & Business Media
Total Pages: 181
Release: 2012-12-06
Genre: Mathematics
ISBN: 3642619703

From the reviews: "This book presents an important and novel approach to Jordan algebras. [...] Springer's work will be of service to research workers familiar with linear algebraic groups who find they need to know something about Jordan algebras and will provide Jordan algebraists with new techniques and a new approach to finite-dimensional algebras over fields." American Scientist

Jordan Algebras and Algebraic Groups

Jordan Algebras and Algebraic Groups
Author: Tonny A. Springer
Publisher: Springer Science & Business Media
Total Pages: 202
Release: 1997-12-11
Genre: Mathematics
ISBN: 9783540636328

From the reviews: "This book presents an important and novel approach to Jordan algebras. [...] Springer's work will be of service to research workers familiar with linear algebraic groups who find they need to know something about Jordan algebras and will provide Jordan algebraists with new techniques and a new approach to finite-dimensional algebras over fields." American Scientist

Octonions, Jordan Algebras and Exceptional Groups

Octonions, Jordan Algebras and Exceptional Groups
Author: Tonny A. Springer
Publisher: Springer
Total Pages: 212
Release: 2013-12-21
Genre: Mathematics
ISBN: 3662126222

The 1963 Göttingen notes of T. A. Springer are well known in the field but have been unavailable for some time. This book is a translation of those notes, completely updated and revised. The part of the book dealing with the algebraic structures is on a fairly elementary level, presupposing basic results from algebra.

A Taste of Jordan Algebras

A Taste of Jordan Algebras
Author: Kevin McCrimmon
Publisher: Springer Science & Business Media
Total Pages: 584
Release: 2006-05-29
Genre: Mathematics
ISBN: 0387217967

This book describes the history of Jordan algebras and describes in full mathematical detail the recent structure theory for Jordan algebras of arbitrary dimension due to Efim Zel'manov. Jordan algebras crop up in many surprising settings, and find application to a variety of mathematical areas. No knowledge is required beyond standard first-year graduate algebra courses.

Lie Groups and Algebraic Groups

Lie Groups and Algebraic Groups
Author: Arkadij L. Onishchik
Publisher: Springer Science & Business Media
Total Pages: 347
Release: 2012-12-06
Genre: Mathematics
ISBN: 364274334X

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.

Lie Algebras and Algebraic Groups

Lie Algebras and Algebraic Groups
Author: Patrice Tauvel
Publisher: Springer Science & Business Media
Total Pages: 650
Release: 2005-08-08
Genre: Mathematics
ISBN: 3540274278

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.

Actions and Invariants of Algebraic Groups

Actions and Invariants of Algebraic Groups
Author: Walter Ricardo Ferrer Santos
Publisher: CRC Press
Total Pages: 479
Release: 2017-09-19
Genre: Mathematics
ISBN: 1482239167

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.

Algebraic Groups

Algebraic Groups
Author: J. S. Milne
Publisher: Cambridge University Press
Total Pages: 665
Release: 2017-09-21
Genre: Mathematics
ISBN: 1107167485

Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.

Linear Algebraic Groups

Linear Algebraic Groups
Author: T.A. Springer
Publisher: Springer Science & Business Media
Total Pages: 347
Release: 2010-10-12
Genre: Mathematics
ISBN: 0817648402

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.

Representations of Algebraic Groups

Representations of Algebraic Groups
Author: Jens Carsten Jantzen
Publisher: American Mathematical Soc.
Total Pages: 594
Release: 2003
Genre: Mathematics
ISBN: 082184377X

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.