Linear Algebraic Groups (Progress in Mathematics 9)

Springer, T.A.

ISBN 10: 0817648399 / ISBN 13: 9780817648398

Editore: Birkhauser Verlag.2009. Reprint of the 1998 second edition., 2008

Riguardo questo articolo

Paperback. Very good. Xii,334pp. Codice articolo 112915

Dati bibliografici

Titolo: Linear Algebraic Groups (Progress in ...

Casa editrice: Birkhauser Verlag.2009. Reprint of the 1998 second edition.

Data di pubblicazione: 2008

Legatura: Brossura

Condizione: Gebraucht / Used

Edizione: seconda edizione

Descrizione articolo

Riassunto:

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.

Dalla quarta di copertina:

<p><em>"[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 literature…appear for the first time in a text."&nbsp;&nbsp; </em><em><strong>–Mathematical Reviews </strong>(Review&nbsp;of the Second Edition)</em></p><p><em>"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."&nbsp;&nbsp; </em><em><strong>–Zentralblatt Math </strong>(Review of the Second Edition)</em></p>