A ternary algebra arising from association schemes on triples
type: Item
instance of: scholarly article
title: A ternary algebra arising from association schemes on triples
zbMATH Open document ID: 0853.17001
author: Dale M. Mesner
author: Prabir Bhattacharya
published in: Journal of Algebra
publication date: 1994-06-29T00:00:00Z
review text: In a previous paper [J. Comb. Theory, Ser. A 55, 204-234 (1990; Zbl 0761.05098)], the authors considered a ternary analogue of association schemes involving ternary (instead of binary) relations and proved that the 3-dimensional adjacency matrices of the relations of the scheme form a ternary algebra under a suitable composition. This may be considered as the ternary analogue of the well-known Bose-Mesner algebra of an ordinary association scheme. Examples were obtained from the groups \(\text{PSL} (2,q)\), \(\text{AGL} (1,q)\) and from 2-designs. In the paper under review, the authors study ternary algebras formed by three-dimensional arrays in general, with particular emphasis on so-called identity pairs and inverse pairs. Some more concrete examples are also discussed in detail.
Mathematics Subject Classification ID: 17A40
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 20N10
zbMATH DE Number: 579541
zbMATH Keywords: association scheme on triples
zbMATH Keywords: designs
zbMATH Keywords: ternary algebra
zbMATH Keywords: Bose-Mesner algebra
reviewed by: Dieter Jungnickel
MaRDI profile type: Publication
full work available at URL: jabr.1994.1081
OpenAlex ID: W2073712460
DOI: 10.1006/JABR.1994.1081
description: scientific article; zbMATH DE number 579541