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AAA76 - 76th Workshop on General Algebra (76. Arbeitstagung Allgemeine Algebra)
May 22-25, 2008
Department of Algebra, Johannes Kepler University Linz
Linz, Austria

Organizers
Erhard Aichinger, Peter Mayr, Matt Nickodemus, Günter Pilz

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Some Generalizations of Bose-Mesner Algebras
by
Armenak S. Gasparyan
Pereslavl-Zalesskii, Russia

For a given permutation group G, G ⊆ Sn1×...×Snl, where Snr be symmetric group of order nr, we introduce the many-sorted partial algebra MGn1, ..., nl(K), of G-symmetric multidimensional matrices over a field K, with a family of operations being the combinations of standard tensor, Cayley and scalar multiplications. The particular type subalgebras yield nontrivial generalizations of Bose-Mesner algebras and related structures such as association schemes, cellular rings, coding schemes, incidence structures and some other. Aim of talk is to reveal some new aspects and problems arising by such generalizations.

Date received: March 12, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawc-17.