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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

MSC:

20N05 Loops, quasigroups
20C99 Representation theory of groups

Citations:

Zbl 0667.20053
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References:

[1] Aigner, M., Kombinatorik I, (1975), Springer-Verlag Berlin
[2] Bannai, E.; Ito, T., Alebraic combinatorics I: association schemes, (), Benjamin-Cummings, Menlo Park, Calif.
[3] Delsarte, P., An algebraic approach to the association schemes of coding theory, Philips res. rep. suppl., 10, (1973) · Zbl 1075.05606
[4] Hagemann, J.; Herrmann, C., A concrete ideal multiplication for algebraic systems and its relation to congruence distributivity, Arch. math.,, 32, 234-245, (1979) · Zbl 0419.08001
[5] Herrmann, C., Affine algebras in congruence modular varieties, Acta sci. math.,, 41, 119-125, (1979) · Zbl 0408.08003
[6] Johnson, K.W.; Smith, J.D.H., Characters of finite quasigroups, Europ. J. combin.,, 5, 43-50, (1984) · Zbl 0537.20042
[7] Johnson, K.W.; Smith, J.D.H., Characters of finite quasigroups II: induced characters, Europ. J. combin.,, 7, 131-137, (1986) · Zbl 0599.20110
[8] Johnson, K.W.; Smith, J.D.H., A note on character induction in association schemes, Europ. J. combin.,, 7, 139, (1986) · Zbl 0656.20066
[9] K. W. Johnson and J. D. H. Smith, Characters of finite quasigroups III: quotients and fusion, Europ. J. Combin., to appear. · Zbl 0667.20053
[10] Serre, J.-P., (), (tr. L. L. Scott)
[11] Smith, J.D.H., Representation theory of infinite groups and finite quasigroups, () · Zbl 0335.20035
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