The Algebraic K-theory of the Classical Groups and Some Twisted Forms
Author: Marc Levine
Publisher:
Published: 1990
Total Pages: 50
ISBN-13:
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Author: Marc Levine
Publisher:
Published: 1990
Total Pages: 50
ISBN-13:
DOWNLOAD EBOOKAuthor: Alexander J. Hahn
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 589
ISBN-13: 3662131528
DOWNLOAD EBOOKIt is a great satisfaction for a mathematician to witness the growth and expansion of a theory in which he has taken some part during its early years. When H. Weyl coined the words "classical groups", foremost in his mind were their connections with invariant theory, which his famous book helped to revive. Although his approach in that book was deliberately algebraic, his interest in these groups directly derived from his pioneering study of the special case in which the scalars are real or complex numbers, where for the first time he injected Topology into Lie theory. But ever since the definition of Lie groups, the analogy between simple classical groups over finite fields and simple classical groups over IR or C had been observed, even if the concept of "simplicity" was not quite the same in both cases. With the discovery of the exceptional simple complex Lie algebras by Killing and E. Cartan, it was natural to look for corresponding groups over finite fields, and already around 1900 this was done by Dickson for the exceptional Lie algebras G and E • However, a deep reason for this 2 6 parallelism was missing, and it is only Chevalley who, in 1955 and 1961, discovered that to each complex simple Lie algebra corresponds, by a uniform process, a group scheme (fj over the ring Z of integers, from which, for any field K, could be derived a group (fj(K).
Author:
Publisher: American Mathematical Soc.
Published: 1991
Total Pages: 186
ISBN-13: 9780821873113
DOWNLOAD EBOOKAuthor: Vasudevan Srinivas
Publisher: Springer Science & Business Media
Published: 2009-05-21
Total Pages: 357
ISBN-13: 0817647392
DOWNLOAD EBOOKAlgebraic K-Theory has become an increasingly active area of research. With its connections to algebra, algebraic geometry, topology, and number theory, it has implications for a wide variety of researchers and students in mathematics. This book is based on lectures given by the author at the Tata Institute in Bombay and elsewhere. This new edition includes an appendix on algebraic geometry that contains required definitions and results needed to understand the core of the book.
Author: Aderemi Kuku
Publisher: CRC Press
Published: 2016-04-19
Total Pages: 442
ISBN-13: 142001112X
DOWNLOAD EBOOKRepresentation Theory and Higher Algebraic K-Theory is the first book to present higher algebraic K-theory of orders and group rings as well as characterize higher algebraic K-theory as Mackey functors that lead to equivariant higher algebraic K-theory and their relative generalizations. Thus, this book makes computations of higher K-theory of grou
Author: Wolfgang Lück
Publisher: Springer
Published: 2006-11-14
Total Pages: 455
ISBN-13: 3540468277
DOWNLOAD EBOOKThe book focuses on the relation between transformation groups and algebraic K-theory. The general pattern is to assign to a geometric problem an invariant in an algebraic K-group which determines the problem. The algebraic K-theory of modules over a category is studied extensively and appplied to the fundamental category of G-space. Basic details of the theory of transformation groups sometimes hard to find in the literature, are collected here (Chapter I) for the benefit of graduate students. Chapters II and III contain advanced new material of interest to researchers working in transformation groups, algebraic K-theory or related fields.
Author: Emilio Lluis-Puebla
Publisher: Springer
Published: 2006-11-14
Total Pages: 172
ISBN-13: 3540466398
DOWNLOAD EBOOKThis book is a general introduction to Higher Algebraic K-groups of rings and algebraic varieties, which were first defined by Quillen at the beginning of the 70's. These K-groups happen to be useful in many different fields, including topology, algebraic geometry, algebra and number theory. The goal of this volume is to provide graduate students, teachers and researchers with basic definitions, concepts and results, and to give a sampling of current directions of research. Written by five specialists of different parts of the subject, each set of lectures reflects the particular perspective ofits author. As such, this volume can serve as a primer (if not as a technical basic textbook) for mathematicians from many different fields of interest.
Author: Hyman Bass
Publisher: World Scientific
Published: 1999-03-12
Total Pages: 622
ISBN-13: 9814544795
DOWNLOAD EBOOKThe Proceedings volume is divided into two parts. The first part consists of lectures given during the first two weeks devoted to a workshop featuring state-of-the-art expositions on 'Overview of Algebraic K-theory' including various constructions, examples, and illustrations from algebra, number theory, algebraic topology, and algebraic/differential geometry; as well as on more concentrated topics involving connections of K-theory with Galois, etale, cyclic, and motivic (co)homologies; values of zeta functions, and Arithmetics of Chow groups and zero cycles. The second part consists of research papers arising from the symposium lectures in the third week.
Author: Hyman Bass
Publisher: Springer
Published: 2006-11-15
Total Pages: 536
ISBN-13: 3540377700
DOWNLOAD EBOOKAuthor: R. Keith Dennis
Publisher: American Mathematical Soc.
Published: 1992
Total Pages: 250
ISBN-13: 0821851306
DOWNLOAD EBOOKIn the mid-1960's, several Italian mathematicians began to study the connections between classical arguments in commutative algebra and algebraic geometry, and the contemporaneous development of algebraic K-theory in the US. These connections were exemplified by the work of Andreotti-Bombieri, Salmon, and Traverso on seminormality, and by Bass-Murthy on the Picard groups of polynomial rings. Interactions proceeded far beyond this initial point to encompass Chow groups of singular varieties, complete intersections, and applications of K-theory to arithmetic and real geometry. This volume contains the proceedings from a US-Italy Joint Summer Seminar, which focused on this circle of ideas. The conference, held in June 1989 in Santa Margherita Ligure, Italy, was supported jointly by the Consiglio Nazionale delle Ricerche and the National Science Foundation. The book contains contributions from some of the leading experts in this area.