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25 Remote Warehouse Mathematics- Group Theory

Blocks of Finite Groups: The Hyperfocal Subalgebra of a Block (Springer Monographs in Mathematics)

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Blocks of Finite Groups: The Hyperfocal Subalgebra of a Block (Springer Monographs in Mathematics) Cover

 

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Publisher Comments:

About 60 years ago, R. Brauer introduced "block theory"; his purpose was to study the group algebra kG of a finite group G over a field k of nonzero characteristic p: any indecomposable two-sided ideal that also is a direct summand of kG determines a G-block. But the main discovery of Brauer is perhaps the existence of families of infinitely many nonisomorphic groups having a "common block"; i.e., blocks having mutually isomorphic "source algebras". In this book, based on a course given by the author at Wuhan University in 1999, all the concepts mentioned are introduced, and all the proofs are developed completely. Its main purpose is the proof of the existence and the uniqueness of the "hyperfocal subalgebra" in the source algebra. This result seems fundamental in block theory; for instance, the structure of the source algebra of a nilpotent block, an important fact in block theory, can be obtained as a corollary. The exceptional layout of this bilingual edition featuring 2 columns per page (one English, one Chinese) sharing the displayed mathematical formulas is the joint achievement of the author and A. Arabia.

Table of Contents

I. Introduction.- II. Lifting idempotents.- III. Points of the O-algebras and multiplicity of the points.- IV. Divisors on N-interior G-algebras.- V. Restriction and induction of divisors.- VI. Local pointed groups on N-interior G-algebras.- VII. On Green's indecomposability theorem.- VIII. Fusions in N-interior G-algebras.- IX. N-interior G-algebras through G-interior algebras.- X. The group algebra.- XI. Fusion Z-algebra of a block.- XII. Source algebras of blocks.- XIII. Local structure of the hyperfocal subalgebra.- XIV. Uniqueness of the hyperfocal subalgebra.- XV. Existence of the hyperfocal subalgebra.- XVI. On the exponential and logarithmic functions in O-algebras.

Product Details

ISBN:
9783642078026
Author:
Puig, Lluis
Publisher:
Springer
Location:
Berlin, Heidelberg
Subject:
Group Theory
Subject:
Group
Subject:
Block
Subject:
hyperfocal algebra
Subject:
source algebra
Subject:
Group Theory and Generalizations The exceptional layout of this bilingual edition featurinmg two colums per page (one English, one Chinese) sharing the displayed mathematical formula, is the joint achievement of the author and A. Arabia.
Subject:
Mathematics-Group Theory
Subject:
Algebra - Abstract
Subject:
Group Theory and Generalizations
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Copyright:
Edition Description:
Softcover reprint of hardcover 1st ed. 2002
Series:
Springer Monographs in Mathematics
Publication Date:
20101207
Binding:
TRADE PAPER
Language:
English
Pages:
220
Dimensions:
235 x 155 mm 345 gr

Related Subjects

Science and Mathematics » Materials Science » General
Science and Mathematics » Mathematics » Algebra » Abstract Algebra
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Group Theory

Blocks of Finite Groups: The Hyperfocal Subalgebra of a Block (Springer Monographs in Mathematics) New Trade Paper
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