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The Classical Groups and K Theory

The Classical Groups and K Theory Author Alexander J. Hahn
ISBN-10 9783662131527
Release 2013-03-09
Pages 578
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It 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).



An Algebraic Introduction to K Theory

An Algebraic Introduction to K Theory Author Bruce A. Magurn
ISBN-10 0521800781
Release 2002-05-20
Pages 676
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An introduction to algebraic K-theory with no prerequisite beyond a first semester of algebra.



Quadratic and Hermitian Forms over Rings

Quadratic and Hermitian Forms over Rings Author Max-Albert Knus
ISBN-10 9783642754012
Release 2012-12-06
Pages 524
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From its birth (in Babylon?) till 1936 the theory of quadratic forms dealt almost exclusively with forms over the real field, the complex field or the ring of integers. Only as late as 1937 were the foundations of a theory over an arbitrary field laid. This was in a famous paper by Ernst Witt. Still too early, apparently, because it took another 25 years for the ideas of Witt to be pursued, notably by Albrecht Pfister, and expanded into a full branch of algebra. Around 1960 the development of algebraic topology and algebraic K-theory led to the study of quadratic forms over commutative rings and hermitian forms over rings with involutions. Not surprisingly, in this more general setting, algebraic K-theory plays the role that linear algebra plays in the case of fields. This book exposes the theory of quadratic and hermitian forms over rings in a very general setting. It avoids, as far as possible, any restriction on the characteristic and takes full advantage of the functorial aspects of the theory. The advantage of doing so is not only aesthetical: on the one hand, some classical proofs gain in simplicity and transparency, the most notable examples being the results on low-dimensional spinor groups; on the other hand new results are obtained, which went unnoticed even for fields, as in the case of involutions on 16-dimensional central simple algebras. The first chapter gives an introduction to the basic definitions and properties of hermitian forms which are used throughout the book.



Buildings

Buildings Author Peter Abramenko
ISBN-10 9780387788357
Release 2008-12-16
Pages 754
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This book treats Jacques Tit's beautiful theory of buildings, making that theory accessible to readers with minimal background. It covers all three approaches to buildings, so that the reader can choose to concentrate on one particular approach. Beginners can use parts of the new book as a friendly introduction to buildings, but the book also contains valuable material for the active researcher. This book is suitable as a textbook, with many exercises, and it may also be used for self-study.



Groups Rings and Group Rings

Groups  Rings and Group Rings Author Antonio Giambruno
ISBN-10 1420010964
Release 2006-01-20
Pages 368
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This book is a collection of research papers and surveys on algebra that were presented at the Conference on Groups, Rings, and Group Rings held in Ubatuba, Brazil. This text familiarizes researchers with the latest topics, techniques, and methodologies in several branches of contemporary algebra. With extensive coverage, it examines broad themes from group theory and ring theory, exploring their relationship with other branches of algebra including actions of Hopf algebras, groups of units of group rings, combinatorics of Young diagrams, polynomial identities, growth of algebras, and more. Featuring international contributions, this book is ideal for mathematicians specializing in these areas.



Structure Theorems of Unit Groups

Structure Theorems of Unit Groups Author Eric Jespers
ISBN-10 9783110411508
Release 2016-01-01
Pages 227
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This two-volume graduate textbook gives a comprehensive, state-of-the-art account of describing large subgroups of the unit group of the integral group ring of a finite group and, more generally, of the unit group of an order in a finite dimensional semisimple rational algebra. Supporting problems illustrate the results and complete some of the proofs. Volume 2 mainly is about structure theorems and geometric methods.



Orders and Generic Constructions of Units

Orders and Generic Constructions of Units Author Eric Jespers
ISBN-10 9783110372946
Release 2016-01-01
Pages 459
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This two-volume graduate textbook gives a comprehensive, state-of-the-art account of describing large subgroups of the unit group of the integral group ring of a finite group and, more generally, of the unit group of an order in a finite dimensional semisimple rational algebra. Supporting problems illustrate the results and complete some of the proofs. Volume 1 contains all details on describing generic constructions of units and their subgroups.



The geometry of the classical groups

The geometry of the classical groups Author Donald E. Taylor
ISBN-10 3885380099
Release 1992
Pages 229
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The geometry of the classical groups has been writing in one form or another for most of life. You can find so many inspiration from The geometry of the classical groups also informative, and entertaining. Click DOWNLOAD or Read Online button to get full The geometry of the classical groups book for free.



Advances in Mathematical Sciences CRM s 25 Years

Advances in Mathematical Sciences  CRM s 25 Years Author Luc Vinet
ISBN-10 0821870130
Release 1997-01-01
Pages 491
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Just list for purposes of NBB.



Manuscripta mathematica

Manuscripta mathematica Author
ISBN-10 UCAL:B4483646
Release 1992
Pages
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Manuscripta mathematica has been writing in one form or another for most of life. You can find so many inspiration from Manuscripta mathematica also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Manuscripta mathematica book for free.



A Computational Theory of Laurent Polynomial Rings and Multidimensional FIR Systems

A Computational Theory of Laurent Polynomial Rings and Multidimensional FIR Systems Author Hyung-Ju Park
ISBN-10 UCAL:C3388543
Release 1995
Pages 252
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A Computational Theory of Laurent Polynomial Rings and Multidimensional FIR Systems has been writing in one form or another for most of life. You can find so many inspiration from A Computational Theory of Laurent Polynomial Rings and Multidimensional FIR Systems also informative, and entertaining. Click DOWNLOAD or Read Online button to get full A Computational Theory of Laurent Polynomial Rings and Multidimensional FIR Systems book for free.



L Enseignement math matique

L Enseignement math  matique Author
ISBN-10 UCAL:B4022824
Release 1989
Pages
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Vols. for 1965- include a separately paged section, Bulletin bibliographique.



Memorandum

Memorandum Author
ISBN-10 UCAL:C3572466
Release 2001
Pages
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Memorandum has been writing in one form or another for most of life. You can find so many inspiration from Memorandum also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Memorandum book for free.



S ri kagaku k ky roku

S  ri kagaku k  ky  roku Author
ISBN-10 UOM:39015049304689
Release 1998
Pages
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S ri kagaku k ky roku has been writing in one form or another for most of life. You can find so many inspiration from S ri kagaku k ky roku also informative, and entertaining. Click DOWNLOAD or Read Online button to get full S ri kagaku k ky roku book for free.



Mathematical Reviews

Mathematical Reviews Author
ISBN-10 UVA:X006088967
Release 2000
Pages
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Mathematical Reviews has been writing in one form or another for most of life. You can find so many inspiration from Mathematical Reviews also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Mathematical Reviews book for free.



Handbook of Incidence Geometry

Handbook of Incidence Geometry Author Francis Buekenhout
ISBN-10 044488355X
Release 1995
Pages 1420
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This Handbook deals with the foundations of incidence geometry, in relationship with division rings, rings, algebras, lattices, groups, topology, graphs, logic and its autonomous development from various viewpoints. Projective and affine geometry are covered in various ways. Major classes of rank 2 geometries such as generalized polygons and partial geometries are surveyed extensively. More than half of the book is devoted to buildings at various levels of generality, including a detailed and original introduction to the subject, a broad study of characterizations in terms of points and lines, applications to algebraic groups, extensions to topological geometry, a survey of results on diagram geometries and nearby generalizations such as matroids.



The Bloch Kato Conjecture for the Riemann Zeta Function

The Bloch Kato Conjecture for the Riemann Zeta Function Author John Coates
ISBN-10 9781107492967
Release 2015-03-13
Pages 320
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A graduate-level account of an important recent result concerning the Riemann zeta function.