On Normalized Integral Table Algebras (Fusion Rings) Generated by a

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 mod

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Algebra and Applications Volume 16

Series Editors: Alice Fialowski Eötvös Loránd University, Budapest, Hungary Eric Friedlander Northwestern University, Evanston, USA John Greenlees Sheffield University, Sheffield, UK Gerhard Hiß Aachen University, Aachen, Germany Ieke Moerdijk Utrecht University, Utrecht, The Netherlands Idun Reiten Norwegian University of Science and Technology, Trondheim, Norway Christoph Schweigert Hamburg University, Hamburg, Germany Mina Teicher Bar-llan University, Ramat-Gan, Israel Alain Verschoren University of Antwerp, Antwerp, Belgium Algebra and Applications aims to publish well written and carefully refereed monographs with up-to-date information about progress in all fields of algebra, its classical impact on commutative and noncommutative algebraic and differential geometry, K-theory and algebraic topology, as well as applications in related domains, such as number theory, homotopy and (co)homology theory, physics and discrete mathematics. Particular emphasis will be put on state-of-the-art topics such as rings of differential operators, Lie algebras and super-algebras, group rings and algebras, C ∗ -algebras, Kac-Moody theory, arithmetic algebraic geometry, Hopf algebras and quantum groups, as well as their applications. In addition, Algebra and Applications will also publish monographs dedicated to computational aspects of these topics as well as algebraic and geometric methods in computer science.

Zvi Arad  Xu Bangteng  Guiyun Chen Effi Cohen  Arisha Haj Ihia Hussam  Mikhail Muzychuk

On Normalized Integral Table Algebras (Fusion Rings) Generated by a Faithful Non-real Element of Degree 3



Zvi Arad Department of Mathematics Bar Ilan University Ramat Gan, 52900 Israel and Netanya Academic College 1 University Street Netanya Israel [email protected] Xu Bangteng Department of Mathematics and Statistics Eastern Kentucky University Richmond, KY, 40475 USA [email protected] Guiyun Chen Department of Mathematics Southwest University Chongqing, 400715 People’s Republic of China [email protected]

Effi Cohen Department of Mathematics Bar Ilan University Ramat Gan, 52900 Israel [email protected] Arisha Haj Ihia Hussam Department of Mathematics Alqasemi Academic College of Education Baqa El-Gharbieh, 30100 Israel [email protected] Mikhail Muzychuk Netanya Academic College Kibbutz Galuyot 16 Netanya, 42 365 Israel [email protected]

ISSN 1572-5553 e-ISSN 2192-2950 ISBN 978-0-85729-849-2 e-ISBN 978-0-85729-850-8 DOI 10.1007/978-0-85729-850-8 Springer London Dordrecht Heidelberg New York British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Control Number: 2011934389 Mathematics Subject Classification: 05E10, 05E30, 13A99, 20C15, 20N20, 81T40 © Springer-Verlag London Limited 2011 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988