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On amorphic C-algebras

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Ilia Ponomarenko, A. Rahnamai Barghi

Combinatorics · Submitted 5 Nov 2005

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this paper we generalize the property to be amorphic to an arbitrary C-algebra and prove that any amorphic C-algebra is determined up to isomorphism by the multiset of its degrees and an additional integer equal 1 or -1.

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arXiv IDmath/0511129 (version 2)
Pith IDKMKTHRH6, Pith's permanent record of this paper and its review
CitationA. Rahnamai Barghi, Ilia Ponomarenko. "On amorphic C-algebras." arXiv:math/0511129 (2005). https://pith.science/paper/KMKTHRH6
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arXiv listing abstract v2. Results and the main claim are underlined; .

An amorphic association scheme has the property that any of its fusion is also an association scheme. In this paper we generalize the property to be amorphic to an arbitrary C-algebra and prove that any amorphic C-algebra is determined up to isomorphism by the multiset of its degrees and an additional integer equal 1 or -1. Moreover, we show that any amorphic C-algebra with rational structure constants is the fusion of an amorphic homogeneous C-algebra. Finally, as a special case of our results we obtain the well-known Ivanov's characterization of intersection numbers of amorphic association schemes.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 An amorphic association scheme has the property that any of its fusion is also an association scheme. background 1.00 0.07 0.03 asserted 1.00
s1 In this paper we generalize the property to be amorphic to an arbitrary C-algebra and prove that any amorphic C-algebra is determined up to isomorphism by the multiset of its degrees and an additional integer equal 1 or -1. contribution 0.77 0.96 0.84 asserted 1.00
s2 Moreover, we show that any amorphic C-algebra with rational structure constants is the fusion of an amorphic homogeneous C-algebra. result 0.99 0.94 0.09 asserted 1.00
s3 Finally, as a special case of our results we obtain the well-known Ivanov's characterization of intersection numbers of amorphic association schemes. result 0.89 0.83 0.07 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Original abstract

An amorphic association scheme has the property that any of its fusion is also an association scheme. In this paper we generalize the property to be amorphic to an arbitrary C-algebra and prove that any amorphic C-algebra is determined up to isomorphism by the multiset of its degrees and an additional integer equal 1 or -1. Moreover, we show that any amorphic C-algebra with rational structure constants is the fusion of an amorphic homogeneous C-algebra. Finally, as a special case of our results we obtain the well-known Ivanov's characterization of intersection numbers of amorphic association schemes.

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