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Dual multivalued groups. (English. Russian original) Zbl 1196.20070
Russ. Math. Surv. 64, No. 5, 955-957 (2009); translation from Usp. Mat. Nauk 64, No. 5, 183-184 (2009).
From the introduction: This note concerns the construction of duality in the theory of multivalued groups. Using the relationships between multivalued groups and both algebraic combinatorics and conventional group and representation theory, we investigate the connections between the duality constructed here and the classical dualities in those areas, namely, the Pontryagin and Kawada-Delsarte dualities. For multivalued groups, the duality constructed here is a first step in the study of the problem (for a more general class of objects) that A. M. Vershik [Funct. Anal. Appl. 41, No. 2, 99-114 (2007); translation from Funkts. Anal. Prilozh. 41, No. 2, 24-43 (2007; Zbl 1184.16034)] called the problem of dilation of comultiplications.

MSC:
20N20 Hypergroups
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
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