The study of the properties of products of conjugacy classes of finite groups is an old branch of finite group theory. This topic was extensively studied in the 1980's. The book Products of Conjugacy classes in Groups, edited by Z. Arad and M. Herzog, volume 1112 of Lecture Notes in Mathematics, Springer, provides a comprehensive picture of the results obtained during this period. 

It was realized by several researchers that this investigation could be extended to products of irreducible characters. This led to the notion of Table Algebra, introduced by Z. Arad and H. Blau in 1991, in order to study in a uniform way the decomposition of products of conjugacy classes Cla(G) and irreducible characters Irr(G) of finite groups G. Since then the theory of Table Algebras has been extensively developed. Today the theory of Table Algebras is an important branch of modern algebra. 

In my lecture I will state the classification theorem of Normalized Integral Table Algebras (Fusion Rings) generated by a faithful non-real element of degree3.

Professor Arad, together with his colleague Professor Marcel Herzog, wrote the book Products of Conjugacy Classes, published by Springer Verlag. The book facilitated the basis of the establishment of mathematical theory and today forms part of the Modern Algebra branch known as Table Algebras, and is attached to central branches in mathematics: Graph theory, Algebracombinations and theory presentation. Professor Arad is counted amongst the leaders in this field. Professor Arad hascomplied three further books with colleagues on the subject of table algebra. In 2000 his book was published in the series American Mathematical Society Memoirs and in January 2002 another book on table algebras was published in the international publication, Springe. In 2011 Professor Arad published the book "On Normalized Integral Table Algebra (Fusion Rings). Jointly with Xu Bangteng, Guiyan Chen, Effi Choen, Arisha Haj Ihia a Hussam, Mikail Muzyshuk. In the Series Algebra and Applications, Springer. Professor Arad has had some 90 articles published in various prestigious international journals. 

Since 1994 till 2012 he has served on the editorial board of the Algebra Colloquium, a journal of the Chinese Academy published by Springer Verlag. He also serves on the editorial board of various international publications: South East Asian Bulletin of Mathematics of the Asian Mathematical Society, the IMCP of Contemporary Mathematics published by the American Mathematical Society, and the publication Cubo Matematica Educacional, Temuco – Chile. 

Professor Arad has held a variety of senior academic posts; including at Bar Ilan University as Head of the Mathematics and Computer Science Department, Dean of the Faculty of Natural Sciences and Mathematics, Rector, and President of the University. Together with ProfessorBernard Pinchukhe founded and established "Gelbart Institute" a prestigious international research institute and the "Emmy Noether Institute" (Minerva Center). Together with colleagues he established the Mathematic journal – Israel Mathematics Conference Proceedings, distributed by the (AMS) American Mathematical Society. From 1984-1985 he served as a member of the Council for Higher Education of the State of Israel. In 1996 together with his colleagues, Professor Deutch and Professor Pinchuk, he initiated and founded Netanya Academic College of which he serves as President. In 1982 he was elected a member of Russia's Academy of Natural Sciences. 

In the Haaretz newspaper (21/1/98) he was described as one of the pioneers in the reform of higher education in Israel. The Hebrew Encyclopedia lists Zvi Arad as "fulfilling a key role in the development and advancement of Bar Ilan University and in the establishment of the University's regional colleges in Sefad, Ashkelon and Emek Hayarden (the Jordan Valley). For this achievement he was awarded a certificate of honor by the Mayor of each city. The establishment of these colleges began in 1985 and went on to affect the whole of Israel. These colleges advanced the Galilee and Southern Israel and brought higher education to the peripheries of the State of Israel.