Generalized table algebras
type: Item
instance of: scholarly article
title: Generalized table algebras
zbMATH Open document ID: 0952.20009
DOI: 10.1007/BF02785571
author: Zvi Arad
author: Elsa Fisman
author: Mikhail Muzychuk
published in: Israel Journal of Mathematics
publication date: 2001-01-11T00:00:00Z
review text: \textit{Y. Kawada} [Proc. Phys.-Math. Soc. Jap., III. Ser. 24, 97-109 (1942)] defined the concept of a \(C\)-algebra to study the common properties of characters and conjugacy classes in finite groups. The concept of a table algebra was defined by \textit{Z. Arad} and \textit{H. I. Blau} [J. Algebra 138, No. 1, 137-185 (1991; Zbl 0790.20015)] and many interesting results about finite groups were obtained in this context. \(C\)-algebras and table algebras are commutative and they are defined over the complex field \(\mathbb{C}\). In [Algebra Colloq. 5, No. 1, 85-97 (1998; Zbl 0948.20003)] the authors of the present paper studied \(C\)-algebras over the complex field without the assumption of the commutativity of the algebra. In the paper under review they define the concept of an algebra, called a generalized table algebra, similar to that of a noncommutative table algebra but letting the ground field be an integral domain. In this paper interesting results concerning generalized table algebras including their representation theory are obtained.
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 16P10
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 20C08
zbMATH DE Number: 1415558
zbMATH Keywords: characters
zbMATH Keywords: conjugacy classes
zbMATH Keywords: finite groups
zbMATH Keywords: \(C\)-algebras
zbMATH Keywords: generalized table algebras
reviewed by: M. R. Darafsheh
MaRDI profile type: Publication
cites work: On table algebras and applications to finite group theory
cites work: Table algebras and applications to products of characters in finite groups
cites work: Real table algebras and applications to finite groups of extended Camina-Frobenius type
cites work: On table algebras, c-algebras, and applications to finite group theory∗
cites work: Q4225656
cites work: Q3218140
cites work: Erratum: Quotient structures in \(C\)-algebras
cites work: Integral table algebras, affine diagrams, and the analysis of degree two
cites work: Q3992965
cites work: Finite Permutation Groups and Finite Simple Groups
cites work: Q4284633
cites work: Coherent algebras
cites work: Q3998721
cites work: Q5843905
cites work: The Finite Primitive Permutation Groups of Rank Three
cites work: Q4374827
cites work: Q5617749
cites work: Q5512231
full work available at URL: https://doi.org/10.1007/bf02785571
OpenAlex ID: W2067462081
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description: scientific article; zbMATH DE number 1415558