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.
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"In the book under review the authors' aim is to classify normalized integral table algebras generated by a faithful non-real element of degree 3. To do this several cases appear and the authors examine each case carefully to prove the existence of the table algebra in question. ... is well organized and will be beneficial to many researchers of finite group theory." (Mohammad-Reza Darafsheh, Mathematical Reviews, Issue 2012 f)