Characters of finite quasigroups. IV: Products and superschemes. (English) Zbl 0669.20053

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.
Reviewer: C.Pereira da Silva


20N05 Loops, quasigroups
20C99 Representation theory of groups


Zbl 0667.20053
Full Text: DOI


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