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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

Normal cyclotomic schemes over a finite commutative ring


Authors: S. Evdokimov and I. Ponomarenko
Translated by: the authors
Original publication: Algebra i Analiz, tom 19 (2007), nomer 6.
Journal: St. Petersburg Math. J. 19 (2008), 911-929
MSC (2000): Primary 13M99
Published electronically: August 21, 2008
MathSciNet review: 2411639
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Abstract: Cyclotomic association schemes over a finite commutative ring $ R$ with identity are studied. The main goal is to identify the normal cyclotomic schemes $ \mathcal{C}$, i.e., those for which $ \operatorname{Aut}(\mathcal{C})\le A\Gamma L_1(R)$. The problem reduces to the case where the ring $ R$ is local, and in this case a necessary condition of normality in terms of the subgroup of $ R^\times$ that determines $ \mathcal{C}$ is given. This condition is proved to be sufficient for a large class of local rings including the Galois rings of odd characteristic.


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Additional Information

S. Evdokimov
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
Email: evdokim@pdmi.ras.ru

I. Ponomarenko
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
Email: inp@pdmi.ras.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-08-01027-3
PII: S 1061-0022(08)01027-3
Keywords: Association scheme, cyclotomic schemes
Received by editor(s): June 20, 2007
Published electronically: August 21, 2008
Additional Notes: Partially supported by RFBR (grants nos. 07-01-00485, 05-01-00899, and 06-01-00471), and by NSH (grant no. 4329.2006.1)
Dedicated: To the centenary of the birth of D. K. Faddeev
Article copyright: © Copyright 2008 American Mathematical Society