K Theory Of Finite Groups And Orders
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K Theory Of Finite Groups And Orders
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Author : Richard G. Swan
language : en
Publisher: Springer
Release Date : 2006-11-15
K Theory Of Finite Groups And Orders written by Richard G. Swan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
K Theory Of Finite Groups And Orders
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Author : Richard G. Swan
language : en
Publisher:
Release Date : 2014-01-15
K Theory Of Finite Groups And Orders written by Richard G. Swan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
The Connective K Theory Of Finite Groups
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Author : Robert Ray Bruner
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
The Connective K Theory Of Finite Groups written by Robert Ray Bruner and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Includes a paper that deals the connective K homology and cohomology of finite groups $G$. This title uses the methods of algebraic geometry to study the ring $ku DEGREES*(BG)$ where $ku$ denotes connective complex K-theory. It describes the variety in terms of the category of abelian $p$-subgroups of $G$ for primes $p$ dividing the group
Representation Theory And Higher Algebraic K Theory
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Author : Aderemi Kuku
language : en
Publisher: CRC Press
Release Date : 2006-09-27
Representation Theory And Higher Algebraic K Theory written by Aderemi Kuku and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-27 with Mathematics categories.
Representation 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 group rings more accessible and provides novel techniques for the computations of higher K-theory of finite and some infinite groups. Authored by a premier authority in the field, the book begins with a careful review of classical K-theory, including clear definitions, examples, and important classical results. Emphasizing the practical value of the usually abstract topological constructions, the author systematically discusses higher algebraic K-theory of exact, symmetric monoidal, and Waldhausen categories with applications to orders and group rings and proves numerous results. He also defines profinite higher K- and G-theory of exact categories, orders, and group rings. Providing new insights into classical results and opening avenues for further applications, the book then uses representation-theoretic techniques-especially induction theory-to examine equivariant higher algebraic K-theory, their relative generalizations, and equivariant homology theories for discrete group actions. The final chapter unifies Farrell and Baum-Connes isomorphism conjectures through Davis-Lück assembly maps.
Introduction To Algebraic K Theory
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Author : John Willard Milnor
language : en
Publisher: Princeton University Press
Release Date : 1971
Introduction To Algebraic K Theory written by John Willard Milnor and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.
Algebraic K-theory describes a branch of algebra that centers about two functors. K0 and K1, which assign to each associative ring ∧ an abelian group K0∧ or K1∧ respectively. Professor Milnor sets out, in the present work, to define and study an analogous functor K2, also from associative rings to abelian groups. Just as functors K0 and K1 are important to geometric topologists, K2 is now considered to have similar topological applications. The exposition includes, besides K-theory, a considerable amount of related arithmetic.
A Course In Finite Group Representation Theory
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Author : Peter Webb
language : en
Publisher: Cambridge University Press
Release Date : 2016-08-19
A Course In Finite Group Representation Theory written by Peter Webb and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-19 with Mathematics categories.
This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.
Algebraic K Theory
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Author : Michael R. Stein
language : en
Publisher: Springer
Release Date : 2006-11-14
Algebraic K Theory written by Michael R. Stein and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
An Algebraic Introduction To K Theory
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Author : Bruce A. Magurn
language : en
Publisher: Cambridge University Press
Release Date : 2002-05-20
An Algebraic Introduction To K Theory written by Bruce A. Magurn and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-05-20 with Mathematics categories.
This is an introduction to algebraic K-theory with no prerequisite beyond a first semester of algebra (including Galois theory and modules over a principal ideal domain). The presentation is almost entirely self-contained, and is divided into short sections with exercises to reinforce the ideas and suggest further lines of inquiry. No experience with analysis, geometry, number theory or topology is assumed. Within the context of linear algebra, K-theory organises and clarifies the relations among ideal class groups, group representations, quadratic forms, dimensions of a ring, determinants, quadratic reciprocity and Brauer groups of fields. By including introductions to standard algebra topics (tensor products, localisation, Jacobson radical, chain conditions, Dedekind domains, semi-simple rings, exterior algebras), the author makes algebraic K-theory accessible to first-year graduate students and other mathematically sophisticated readers. Even if your algebra is rusty, you can read this book; the necessary background is here, with proofs.
Representation Theory And Higher Algebraic K Theory
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Author : Aderemi Kuku
language : en
Publisher: CRC Press
Release Date : 2016-04-19
Representation Theory And Higher Algebraic K Theory written by Aderemi Kuku and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Mathematics categories.
Representation 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
K Theory
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Author : Michael Atiyah
language : en
Publisher: CRC Press
Release Date : 2018-03-05
K Theory written by Michael Atiyah and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-05 with Mathematics categories.
These notes are based on the course of lectures I gave at Harvard in the fall of 1964. They constitute a self-contained account of vector bundles and K-theory assuming only the rudiments of point-set topology and linear algebra. One of the features of the treatment is that no use is made of ordinary homology or cohomology theory. In fact, rational cohomology is defined in terms of K-theory.The theory is taken as far as the solution of the Hopf invariant problem and a start is mode on the J-homomorphism. In addition to the lecture notes proper, two papers of mine published since 1964 have been reproduced at the end. The first, dealing with operations, is a natural supplement to the material in Chapter III. It provides an alternative approach to operations which is less slick but more fundamental than the Grothendieck method of Chapter III, and it relates operations and filtration. Actually, the lectures deal with compact spaces, not cell-complexes, and so the skeleton-filtration does not figure in the notes. The second paper provides a new approach to K-theory and so fills an obvious gap in the lecture notes.