On even generalized table algebras

Z. Arad; Y. Erez; M. Muzychuk

doi:10.1023/A:1022930714277

On even generalized table algebras

Z. Arad, Y. Erez, M. Muzychuk

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Generalized table algebras were introduced in Arad, Fisman and Muzychuk (Israel J. Math. 114 (1999), 29-60) as an axiomatic closure of some algebraic properties of the Bose-Mesner algebras of association schemes. In this note we show that if all non-trivial degrees of a generalized integral table algebra are even, then the number of real basic elements of the algebra is bounded from below (Theorem 2.2). As a consequence we obtain some interesting facts about association schemes the non-trivial valencies of which are even. For example, we proved that if all non-identical relations of an association scheme have the same valency which is even, then the scheme is symmetric.

Original language	English
Pages (from-to)	163-170
Number of pages	8
Journal	Journal of Algebraic Combinatorics
Volume	17
Issue number	2
DOIs	https://doi.org/10.1023/A:1022930714277
State	Published - Mar 2003

Bibliographical note

Funding Information:
†The contribution of this author to this paper is a part of his Ph.D. thesis at Bar-Ilan University. ∗This author was partially supported by the Israeli Ministry of Absorption.

Funding

†The contribution of this author to this paper is a part of his Ph.D. thesis at Bar-Ilan University. ∗This author was partially supported by the Israeli Ministry of Absorption.

Funders	Funder number
Ministry of Aliyah and Immigrant Absorption

Keywords

Association schemes
Generalized table algebras

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10.1023/A:1022930714277

Cite this

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AU - Erez, Y.

AU - Muzychuk, M.

N1 - Funding Information: †The contribution of this author to this paper is a part of his Ph.D. thesis at Bar-Ilan University. ∗This author was partially supported by the Israeli Ministry of Absorption.

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N2 - Generalized table algebras were introduced in Arad, Fisman and Muzychuk (Israel J. Math. 114 (1999), 29-60) as an axiomatic closure of some algebraic properties of the Bose-Mesner algebras of association schemes. In this note we show that if all non-trivial degrees of a generalized integral table algebra are even, then the number of real basic elements of the algebra is bounded from below (Theorem 2.2). As a consequence we obtain some interesting facts about association schemes the non-trivial valencies of which are even. For example, we proved that if all non-identical relations of an association scheme have the same valency which is even, then the scheme is symmetric.

AB - Generalized table algebras were introduced in Arad, Fisman and Muzychuk (Israel J. Math. 114 (1999), 29-60) as an axiomatic closure of some algebraic properties of the Bose-Mesner algebras of association schemes. In this note we show that if all non-trivial degrees of a generalized integral table algebra are even, then the number of real basic elements of the algebra is bounded from below (Theorem 2.2). As a consequence we obtain some interesting facts about association schemes the non-trivial valencies of which are even. For example, we proved that if all non-identical relations of an association scheme have the same valency which is even, then the scheme is symmetric.

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On even generalized table algebras

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