Overview

"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."

Full Product Details

Author:   Lluis Puig
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of hardcover 1st ed. 2002
Dimensions:   Width: 15.50cm , Height: 1.20cm , Length: 23.50cm
Weight:   0.454kg
ISBN:  

9783642078026

ISBN 10:   3642078028
Pages:   215
Publication Date:   06 December 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Language:   eng, chi

Table of Contents

1. Introduction.- 2. Lifting Idempotents.- 3. Points of the O-algebras and Multiplicity of the Points.- 4. Divisors on N-interior G-algebras.- 5. Restriction and Induction of Divisors.- 6. Local Pointed Groups on N-interior G-algebras.- 7. On Green’s Indecomposability Theorem.- 8. Fusions in N-interior G-algebras.- 9. N-interior G-algebras through G-interior Algebras.- 10. Pointed Groups on the Group Algebra.- 11. Fusion ?-algebra of a Block.- 12. Source Algebras of Blocks.- 13. Local Structure of the Hyperfocal Subalgebra.- 14. Uniqueness of the Hyperfocal Subalgebra.- 15. Existence of the Hyperfocal Subalgebra.- 16. On the Exponential and Logarithmic Functions in O-algebras.- References.

Reviews

From the reviews: The author's purpose here is to provide a better understanding of the subject, and to make the proofs understandable by students in group theory. The book, which is written in both Chinese (in simple characters) and English, consists of 16 sections. All the concepts are carefully introduced, and the proofs are complete and given in detail, assuming only knowledge of Wedderburn's theorems, Nakayama's Lemma and other basic algebraic topics. (Jian Bei An, Mathematical Reviews, 2003 j) The book ! contains an exposition of the author's main result on the hyperfocal subalgebra of a block. ! The book is bilingual; each page consists of two columns, one with the Chinese and one with the English text. The author has made an effort to make his exposition self-contained ! . Also, the original proof of the main result has been modified and improved at several points. One of the new concepts that is studied ! is that of a divisor on a G-algebra. (Burkhard Kulshammer, Zentralblatt MATH, Vol. 1002 (2), 2003)

From the reviews: The author's purpose here is to provide a better understanding of the subject, and to make the proofs understandable by students in group theory. The book, which is written in both Chinese (in simple characters) and English, consists of 16 sections. All the concepts are carefully introduced, and the proofs are complete and given in detail, assuming only knowledge of Wedderburn's theorems, Nakayama's Lemma and other basic algebraic topics. (Jian Bei An, Mathematical Reviews, 2003 j) The book ... contains an exposition of the author's main result on the hyperfocal subalgebra of a block. ... The book is bilingual; each page consists of two columns, one with the Chinese and one with the English text. The author has made an effort to make his exposition self-contained ... . Also, the original proof of the main result has been modified and improved at several points. One of the new concepts that is studied ... is that of a divisor on a G-algebra. (Burkhard Kulshammer, Zentralblatt MATH, Vol. 1002 (2), 2003)

From the reviews: The author's purpose here is to provide a better understanding of the subject, and to make the proofs understandable by students in group theory. The book, which is written in both Chinese (in simple characters) and English, consists of 16 sections. All the concepts are carefully introduced, and the proofs are complete and given in detail, assuming only knowledge of Wedderburn's theorems, Nakayama's Lemma and other basic algebraic topics. (Jian Bei An, Mathematical Reviews, 2003 j) The book ... contains an exposition of the author's main result on the hyperfocal subalgebra of a block. ... The book is bilingual; each page consists of two columns, one with the Chinese and one with the English text. The author has made an effort to make his exposition self-contained ... . Also, the original proof of the main result has been modified and improved at several points. One of the new concepts that is studied ... is that of a divisor on a G-algebra. (Burkhard Kulshammer, Zentralblatt MATH, Vol. 1002 (2), 2003)

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