Abstract
An amorphic association scheme has the property that any of its fusions also is an association scheme. In this paper, the property of being amorphic is extended to an arbitrary C-algebra, and it is proved that, up to isomorphism, any amorphic C-algebra is determined by the multiset of its diagonal structure constants and an additional integer equal to ±1. It is shown that any amorphic C-algebra with rational structure constants is a fusion of a homogeneous amorphic C-algebra. As a special case, the well-known Ivanov characterization of the intersection numbers of amorphic association schemes is obtained. Bibliography: 13 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 340, 2006, pp. 87–102.
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Ponomarenko, I.N., Rahnamai Barghi, A. On amorphic C-algebras. J Math Sci 145, 4981–4988 (2007). https://doi.org/10.1007/s10958-007-0333-9
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DOI: https://doi.org/10.1007/s10958-007-0333-9