On Normalized Integral Table Algebras (Fusion Rings)
On Normalized Integral Table Algebras (Fusion Rings)
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DOI：
10.1007/978-0-85729-850-8
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Z. Arad;Bangteng Xu;Guiyun Chen;Elisabeth G. Cohen;Arisha Haj Ihia Hussam;M. Muzychuk
中科院分区：
文献类型：
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作者：
Z. Arad;Bangteng Xu;Guiyun Chen;Elisabeth G. Cohen;Arisha Haj Ihia Hussam;M. Muzychuk
表代数理论是由Z. Arad和H. Blau，以便以统一的方式处理有限群的共轭类和不可约特征标的积。今天，表代数理论是现代代数的一个成熟的分支，具有各种应用，包括有限群的表示理论，代数组合学和融合规则代数。这本书介绍了这一领域的最新发展。它的主要目标是给出一个分类的正规化积分表代数（融合环）所产生的一个忠实的非实元素的程度为3。分为4个部分，第一部分概述了分类方法，其余部分分别处理分类过程中出现的特殊情况。一个特别独特的贡献领域，可以发现在第四部分，其中一些代数是链接到多项式不可约表示的群SL 3（C）。这本书将是感兴趣的研究数学家和博士生工作在表代数，群表示理论，代数组合学和积分融合规则代数。
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.