عنوان

The Classical Groups and K-Theory

(Number (ISBN

3662131528

(Number (ISBN

9783662131527

Number

b580885

Title Proper

The Classical Groups and K-Theory

General Material Designation

[Book]

First Statement of Responsibility

by Alexander J. Hahn, O. Timothy O'Meara.

Place of Publication, Distribution, etc.

Berlin, Heidelberg

Name of Publisher, Distributor, etc.

Springer Berlin Heidelberg

Date of Publication, Distribution, etc.

1989

Specific Material Designation and Extent of Item

(xv, 578 pages)

Series Title

Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 291.

Text of Note

Introduction --; Notation and Conventions --; General Linear Groups, Steinberg Groups, and K-Groups --; Linear Groups over Division Rings --; Isomorphism Theory for the Linear Groups --; Linear Groups over General Classes of Rings --; Unitary Groups, Unitary Steinberg Groups, and Unitary K-Groups --; Unitary Groups over Division Rings --; Clifford Algebras and Orthogonal Groups over Commutative Rings --; Isomorphism Theory for the Unitary Groups --; Unitary Groups over General Classes of Form Rings --; Concluding Remarks --; Bibliography --; Index of Concepts --; Index of Symbols.

Text of Note

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 detail. The book also includes a revised and expanded version of Dieudonné's classical theory over division rings. The authors analyse congruence subgroups, normal subgroups and quotient groups, they describe their isomorphisms and investigate connections with linear and hermitian K-theory. A first insight is offered through the simplest case of the general linear group. All the other classical groups, notably the symplectic, unitary and orthogonal groups, are dealt with uniformly as isometry groups of generalized quadratic modules. New results on the unitary Steinberg groups, the associated K2-groups and the unitary symbols in these groups lead to simplified presentation theorems for the classical groups. Related material such as the K-theory exact sequences of Bass and Sharpe and the Merkurjev-Suslin theorem is outlined. From the foreword by J. Dieudonné: "All mathematicians interested in classical groups should be grateful to these two outstanding investigators for having brought together old and new results (many of them their own) into a superbly organized whole. I am confident that their book will remain for a long time the standard reference in the theory."

Group theory.

Mathematics.

Number theory.

by Alexander J. Hahn, O. Timothy O'Meara.

Alexander J Hahn

O Timothy O'Meara

Electronic name

[Book]

Y