On amorphic $C$-algebras
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part I, Tome 340 (2006), pp. 87-102
I. N. Ponomarenko; A. Rahnamai Barghi. On amorphic $C$-algebras. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part I, Tome 340 (2006), pp. 87-102. http://geodesic.mathdoc.fr/item/ZNSL_2006_340_a5/
@article{ZNSL_2006_340_a5,
     author = {I. N. Ponomarenko and A. Rahnamai Barghi},
     title = {On amorphic $C$-algebras},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {87--102},
     year = {2006},
     volume = {340},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_340_a5/}
}
TY  - JOUR
AU  - I. N. Ponomarenko
AU  - A. Rahnamai Barghi
TI  - On amorphic $C$-algebras
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2006
SP  - 87
EP  - 102
VL  - 340
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2006_340_a5/
LA  - ru
ID  - ZNSL_2006_340_a5
ER  - 
%0 Journal Article
%A I. N. Ponomarenko
%A A. Rahnamai Barghi
%T On amorphic $C$-algebras
%J Zapiski Nauchnykh Seminarov POMI
%D 2006
%P 87-102
%V 340
%U http://geodesic.mathdoc.fr/item/ZNSL_2006_340_a5/
%G ru
%F ZNSL_2006_340_a5

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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 diagonal structure constants and an additional integer equal $\pm 1$. We show that any amorphic $C$-algebra with rational structure constants is the fusion of an amorphic homogeneous $C$-algebra. As a special case of our results we obtain the well-known Ivanov's characterization of intersection numbers of amorphic association schemes.

[1] E. Bannai, T. Ito, Algebraicheskaya kombinatorika. Skhemy otnoshenii, Mir, M., 1987 | MR

[2] A. M. Vershik, S. A. Evdokimov, I. N. Ponomarenko, “Algebry v plansherelevoi dvoistvennosti i algebraicheskaya kombinatorika”, Funkts. anal. i ego pril., 31 (1997), 34–46 | MR | Zbl

[3] Ya. Yu. Golfand, M. Kh. Klin, “Amorfnye kletochnye koltsa, I”, Issledovaniya po algebraicheskoi teorii kombinatornykh ob'ektov, VNIISI, M., 1985, 2–38 | MR

[4] A. V. Ivanov, “Amorfnye kletochnye koltsa, II”, Issledovaniya po algebraicheskoi teorii kombinatornykh ob'ektov, VNIISI, M., 1985, 39–49

[5] Z. Arad, H. I. Blau, “On table algebras and applications to finite group theory”, J. Algebra, 138 (1991), 137–185 | DOI | MR | Zbl

[6] Z. Arad, E. Fisman, M. Muzychuk, “Generalized table algebras”, Israel J. Math., 114 (1999), 29–60 | DOI | MR | Zbl

[7] E. Bannai, “Subschemes of some association schemes”, J. Algebra, 144 (1991), 167–188 | DOI | MR | Zbl

[8] E. Bannai, “On a theorem of Ikuta, Ito and Munemasa”, European J. Combin., 13 (1992), 1–3 | DOI | MR | Zbl

[9] L. D. Baumert, W. H. Mills, R. L. Ward, “Uniform cyclotomy”, J. Number Theory, 14 (1982), 67–82 | DOI | MR | Zbl

[10] J. A. Davis, Q. Xiang, “Amorphic association schemes with negative Latin square-type graphs”, Finite Fields Appl., 12 (2006), 595–612 | DOI | MR | Zbl

[11] P. Dembowski, Finite geometries, Springer, Berlin, 1968 | MR

[12] J. D. Dixon, B. Mortimer, Permutation groups, Springer-Verlag, New York, 1994 | MR

[13] T. Ikuta, T. Ito, A. Munemasa, “On pseudo-automorphisms and fusions of an association scheme”, European J. Combin., 12 (1991), 317–325 | MR | Zbl

[14] T. Ito, A. Munemasa, M. Yamada, “Amorphous association schemes over the Galois rings of characteristic $4$”, European J. Combin., 12 (1991), 513–526 | MR | Zbl