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Monday, May 18, 2020 | History

8 edition of The classical groups and K-theory found in the catalog.

The classical groups and K-theory

by Alexander Hahn

  • 202 Want to read
  • 34 Currently reading

Published by Springer-Verlag in Berlin, New York .
Written in English

    Subjects:
  • Linear algebraic groups.,
  • K-theory.

  • Edition Notes

    StatementAlexander J. Hahn, O. Timothy O"Meara ; foreword by J. Dieudonné.
    SeriesGrundlehren der mathematischen Wissenschaften ;, 291
    ContributionsO"Meara, O. T. 1928-
    Classifications
    LC ClassificationsQA171 .H235 1989
    The Physical Object
    Paginationxv, 576 p. ;
    Number of Pages576
    ID Numbers
    Open LibraryOL2035823M
    ISBN 100387177582
    LC Control Number88011958

    Gives a comprehensive account of the basic algebraic properties of the Classical groups over rings. This book also includes a revised and expanded version of Dieudonne's Classical theory over division rings. It analyses congruence subgroups, normal subgroups and quotient groups, and investigates connections with linear and hermitian K-theory. 2. The beginning of K-theory 3. Relation between K-theory and Bott periodicity 4. K-theory as a homology theory on Banach algebras 5. K-theory as a homology theory on discrete rings 1. PRELIMINARIES ON HOMOTOPY THEORY. CLASSICAL BOTT PERIODICITY Let X and Y be two “nice” topological spaces (for instance metric spaces). Two.

      Algebraic \(K\)-theory, which is the main character of this book, deals mainly with studying the structure of rings. However, it turns out that even working in a purely algebraic context, one requires techniques from homotopy theory to construct the higher \(K\)-groups and to perform computations. In the third chapter we give a brief overview of the classical K-theory for K1 and K2 of a ring. Via the Fundamental Theorem, this leads to Bass’ “negative K-theory,” meaning groups K−1, K−2, etc. We cite Matsumoto’s presentation for K2 of a field from Milnor [], and .

    Cite this chapter as: Hahn A.J., O’Meara O.T. () Unitary Groups over Division Rings. In: The Classical Groups and K-Theory. Grundlehren der mathematischen Wissenschaften (A Series of Comprehensive Studies in Mathematics), vol Author: Alexander J. Hahn, O. Timothy O’Meara. groups, some people prefer SO(n) to O(n), and like to call SO(n) a classical group. Others are interested in simply connected groups, or only in the Lie algebra, and so like to call the double cover Spin(n) of SO(n) a classical group. But there are some subtle theorems about O(n) that actually fail File Size: 91KB.


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The classical groups and K-theory by Alexander Hahn Download PDF EPUB FB2

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 by: 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 5/5(1).

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. 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 : Alexander J.

Hahn. 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.

By A. Hahn and T. O'Meara: pp., DM–, ISBN 3 2 (Springer, ).Cited by: Using basic concepts from algebra, he examines the various properties of the groups. Analysis and topology are used wherever appropriate.

The book also covers topics such as matrix algebras, semigroups, In this renowned volume, Hermann Weyl discusses the symmetric, full linear, orthogonal, and symplectic groups and determines their different /5(8).

In The Classical Groups, his most important book, Weyl provided a detailed introduction to the development of group theory, and he did it in a way that motivated and entertained his readers.

Departing from most theoretical mathematics books of the time, he introduced historical events and people as well as theorems and proofs.

In I wrote out a brief outline, following Quillen's paper Higher algebraic K-theory I. It was overwhelming. I talked to Hy Bass, the author of the classic book Algebraic K-theory, about what would be involved in writing such a book.

It was scary, because (in ) I didn't know even how to write a book. The Classical Groups and K-Theory | and O.T.O'Meara | download | B–OK. Download books for free.

Find books. The Classical Groups: Their Invariants and Representations is a mathematics book by Hermann Weyl, which describes classical invariant theory in terms of representation theory.

It is largely responsible for the revival of interest in invariant theory, which had been almost killed off by David Hilbert 's solution of its main problems in the s. 1 The Classical Groups The groups Let F denote either the real numbers, R, or the complex numbers, section we will describe the main players in the rest of this book the Classical Groups as designated by Hermann section should be treated as a dictionary.

The groups as named here will appear throughout the Size: KB. The Classical Groups and K-Theory by Alexander J. Hahn,available at Book Depository with free delivery worldwide.3/5(1). Gives a comprehensive account of the basic algebraic properties of the classical groups over rings.

This book also includes a revised and expanded version of Dieudonne's classical theory. The classical groups. The classical groups are exactly the general linear groups over R, C and H together with the automorphism groups of non-degenerate forms discussed below.

These groups are usually additionally restricted to the subgroups whose elements have determinant 1, so that their centers are discrete. The classical groups, with the determinant 1 condition, are listed in the table below.

remarks on K-theory, which might be interesting for applications. The first K-group measures the difference between the classical group and its subgroup generated by the root elations. The second K-group is a kind of fundamental group of the group generated by the root elations and is related to central extensions.

The Classical Groups and K-Theory. [Alexander J Hahn; O Timothy O'Meara] -- The book gives a comprehensive account of the basic algebraic properties of the classical groups over rings.

Much of the theory appears in book form for the first time, and most proofs are given in. The book offers a comprehensive introduction to Leavitt path algebras (LPAs) and graph C*-algebras. Highlighting their significant connection with classical K-theory—which plays an important role in mathematics and its related emerging fields—this book allows readers from diverse mathematical backgrounds to understand and appreciate these structures.

Classical Groups and Introduction to K-Theory. at IISER Pune To sum it up in words of Alperin while reviewing books on group theory: The typical example of a finite group is GL(n,q), the general linear group of n dimensions over the field with q elements. The student who is introduced to the subject with other examples is being completely.

Read Online Now the classical groups and k theory Ebook PDF at our Library. Get the classical groups and k theory PDF file for free from our online library PDF File: the classical groups and k theory. 3rd Edition PDF.

So depending on what exactly you are searching, you will be able to choose ebooks to suit your own needs. Homology of classical groups and K-theory Homologie van de klassieke groepen en K-theorie (met een samenvatting in het Nederlands) Proefschrift ter verkrijging van de graad van doctor aan de Uni-versiteit Utrecht op gezag van de Rector Magnificus, Prof.

dr. W.H. Gispen, ingevolge het besluit van het College. Abstract Algebra: A First Course. By Dan Saracino I haven't seen any other book explaining the basic concepts of abstract algebra this beautifully.

It is divided in two parts and the first part is only about groups though. The second part is an in.Unlike many other terms in mathematics which have a universally understood meaning (for instance, "group"), the term classical group seems to have a fuzzier definition.

Apparently it originates with Weyl's book The Classical Groups but doesn't make it into the .