Characters of finite quasigroups. IV: Products and superschemes
type: Item
instance of: scholarly article
title: Characters of finite quasigroups. IV: Products and superschemes
zbMATH Open document ID: 0669.20053
DOI: 10.1016/S0195-6698(89)80060-5
author: J. D. H. Smith
author: Kenneth Johnson
published in: European Journal of Combinatorics
publication date: 1989-01-01T00:00:00Z
review text: This paper is part of a series of articles of the authors [Part III cf. ibid. No.1, 47-56 (1989; Zbl 0667.20053)] developing the combinatorial character theory of finite quasigroups and the theory of association schemes on which it depends. The current paper is concerned with character tables of direct products and tensor products of character tables. For finite loops, the character table of a direct product is the tensor product of the character tables of the direct factors. This is no longer true for quasigroups. In last part of the paper, a combinatorial interpretation of the tensor square of a quasigroup character table is obtained in terms of superschemes, a higher-dimensional extension of the concept of association scheme.
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 20C99
zbMATH DE Number: 4095787
zbMATH Keywords: finite quasigroups
zbMATH Keywords: association schemes
zbMATH Keywords: character tables
zbMATH Keywords: direct products
zbMATH Keywords: tensor products
zbMATH Keywords: finite loops
zbMATH Keywords: superschemes
reviewed by: C. Pereira da Silva
MaRDI profile type: Publication
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full work available at URL: s0195-6698(89)80060-5
OpenAlex ID: W2047723194
description: scientific article; zbMATH DE number 4095787