Geodesic
On amorphic $C$-algebras
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part I, Tome 340 (2006), pp. 87-102 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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. 
@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
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/

[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