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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.



A1 Algebraic Topology over a Field

A1 Algebraic Topology over a Field Author Fabien Morel
ISBN-10 9783642295140
Release 2012-07-13
Pages 259
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This text deals with A1-homotopy theory over a base field, i.e., with the natural homotopy theory associated to the category of smooth varieties over a field in which the affine line is imposed to be contractible. It is a natural sequel to the foundational paper on A1-homotopy theory written together with V. Voevodsky. Inspired by classical results in algebraic topology, we present new techniques, new results and applications related to the properties and computations of A1-homotopy sheaves, A1-homology sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties.



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.



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.



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.



S ri kagaku k ky roku

S  ri kagaku k  ky  roku Author
ISBN-10 UOM:39015049304689
Release 1998
Pages
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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.



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.



Elliptic Functions

Elliptic Functions Author Komaravolu Chandrasekharan
ISBN-10 9783642522444
Release 2012-12-06
Pages 192
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This book has grown out of a course of lectures on elliptic functions, given in German, at the Swiss Federal Institute of Technology, Zurich, during the summer semester of 1982. Its aim is to give some idea of the theory of elliptic functions, and of its close connexion with theta-functions and modular functions, and to show how it provides an analytic approach to the solution of some classical problems in the theory of numbers. It comprises eleven chapters. The first seven are function-theoretic, and the next four concern arithmetical applications. There are Notes at the end of every chapter, which contain references to the literature, comments on the text, and on the ramifications, old and new, of the problems dealt with, some of them extending into cognate fields. The treatment is self-contained, and makes no special demand on the reader's knowledge beyond the elements of complex analysis in one variable, and of group theory.



Cyclic Homology

Cyclic Homology Author Jean-Louis Loday
ISBN-10 9783662113899
Release 2013-03-09
Pages 516
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From the reviews: "This is a very interesting book containing material for a comprehensive study of the cyclid homological theory of algebras, cyclic sets and S1-spaces. Lie algebras and algebraic K-theory and an introduction to Connes'work and recent results on the Novikov conjecture. The book requires a knowledge of homological algebra and Lie algebra theory as well as basic technics coming from algebraic topology. The bibliographic comments at the end of each chapter offer good suggestions for further reading and research. The book can be strongly recommended to anybody interested in noncommutative geometry, contemporary algebraic topology and related topics." European Mathematical Society Newsletter In this second edition the authors have added a chapter 13 on MacLane (co)homology.



Encyclopedia of mathematical physics

Encyclopedia of mathematical physics Author Sheung Tsun Tsou
ISBN-10 0125126603
Release 2006-06-06
Pages 3500
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The Encyclopedia of Mathematical Physics provides a complete resource for researchers, students and lecturers with an interest in mathematical physics. It enables readers to access basic information on topics peripheral to their own areas, to provide a repository of the core information in the area that can be used to refresh the researcher's own memory banks, and aid teachers in directing students to entries relevant to their course-work. The Encyclopedia does contain information that has been distilled, organised and presented as a complete reference tool to the user and a landmark to the body of knowledge that has accumulated in this domain. It also is a stimulus for new researchers working in mathematical physics or in areas using the methods originated from work in mathematical physics by providing them with focused high quality background information. * First comprehensive interdisciplinary coverage * Mathematical Physics explained to stimulate new developments and foster new applications of its methods to other fields * Written by an international group of experts * Contains several undergraduate-level introductory articles to facilitate acquisition of new expertise * Thematic index and extensive cross-referencing to provide easy access and quick search functionality * Also available online with active linking.



The K book

The  K  book Author Charles A. Weibel
ISBN-10 9780821891322
Release 2013-06-13
Pages 618
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Informally, $K$-theory is a tool for probing the structure of a mathematical object such as a ring or a topological space in terms of suitably parameterized vector spaces and producing important intrinsic invariants which are useful in the study of algebr