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On Normalized Integral Table Algebras (Fusion Rings) : Generated by a Faithful Non-real Element of Degree 3 / by Zvi Arad, Xu Bangteng, Guiyun Chen, Effi Cohen, Arisha Haj Ihia Hussam, Mikhail Muzychuk
Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Algebra and Applications ; 16 | SpringerLink BücherPublisher: London : Springer-Verlag London Limited, 2011Description: Online-Ressource (X, 274p. 1 illus, digital)ISBN:- 9780857298508
- 512.22 512.24
- 512
- QA150-272
- QA251.3
Contents:
Summary: Introduction -- Splitting the Main Problem into Four Sub-cases -- A Proof of a Non-existence Sub-case (2) -- Preliminary Classification of Sub-case (2) -- Finishing the Proofs of the Main Results.Summary: The theory of table algebras was introduced in 1991 by Z. Arad and H.Blau in order to treat, in a uniform way, products of conjugacy classes and irreducible characters of finite groups. Today, table algebra theory is a well-established branch of modern algebra with various applications, including the representation theory of finite groups, algebraic combinatorics and fusion rules algebras. This book presents the latest developments in this area. Its main goal is to give a classification of the Normalized Integral Table Algebras (Fusion Rings) generated by a faithful non-real element of degree 3. Divided into 4 parts, the first gives an outline of the classification approach, while remaining parts separately treat special cases that appear during classification. A particularly unique contribution to the field, can be found in part four, whereby a number of the algebras are linked to the polynomial irreducible representations of the group SL3(C). This book will be of interest to research mathematicians and PhD students working in table algebras, group representation theory, algebraic combinatorics and integral fusion rule algebras.PPN: PPN: 1651003459Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
On Normalized Integral Table Algebras (Fusion Rings); Preface; Acknowledgements; Contents; Chapter 1: Introduction; References; Chapter 2: Splitting of the Main Problem into Four Sub-cases; 2.1 Introduction; 2.2 Two NITA Generated by a Non-real Element of Degree 3 not Derived from a Group and Lemmas; 2.3 NITA Generated by b3 and Satisfying b23=b4+b5; 2.4 General Information on NITA Generated by b3 and Satisfying b32=b3+b6 and b23=c3+b6; 2.5 NITA Generated by b3 Satisfying b32=b3+b6 and b6 Nonreal and b10B is Real
2.6 NITA Generated by b3 Satisfying b23=c3+b6, c3b3, b3, b6 Non-real, (b3b8, b3b8)=4 and c32=r3+s62.7 Structure of NITA Generated by b3 and Satisfying b23=c3+b6, c3b3, b3, (b3b8, b3b8)=3 and c3 Non-real; 2.8 Structure of NITA Generated by b3 and Satisfying b23=c3+b6, c3b3, b3, (b3b8, b3b8)=3 and c3 Real; References; Chapter 3: A Proof of a Non-existence of Sub-case (2); 3.1 Introduction; 3.2 Preliminary Results; 3.3 Case z = z3; 3.4 Cases z = z4, z = z5, z = z6, z = z7, and z = z8; 3.5 Case z = z9; Chapter 4: Preliminary Classification of Sub-case (3); 4.1 Introduction
4.2 Preliminary Results4.3 Case R15=x5+x10; 4.4 Case R15=x6+x9; 4.5 Case R15=x7+x8; 4.6 Case (b3x7,b3x7)=3; 4.7 Case b3b10=b15+x5+y5+z5; Chapter 5: Finishing the Proofs of the Main Results; 5.1 Introduction; 5.2 Proof of Theorem 5.1; 5.3 Proof of Theorem 5.2; References; Index
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