عنوان

The Classical Groups and K-Theory

شابک

3662131528

شابک

9783662131527

شماره

b580885

عنوان اصلي

The Classical Groups and K-Theory

نام عام مواد

[Book]

نام نخستين پديدآور

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

محل نشرو پخش و غیره

Berlin, Heidelberg

نام ناشر، پخش کننده و غيره

Springer Berlin Heidelberg

تاریخ نشرو بخش و غیره

1989

نام خاص و کميت اثر

(xv, 578 pages)

عنوان فروست

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

متن يادداشت

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.

متن يادداشت

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."

موضوع مستند نشده

Group theory.

موضوع مستند نشده

Mathematics.

موضوع مستند نشده

Number theory.

مستند نام اشخاص تاييد نشده

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

مستند نام اشخاص تاييد نشده

Alexander J Hahn

مستند نام اشخاص تاييد نشده

O Timothy O'Meara

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y