ORTHOGONAL DECOMPOSITIONS AND IDEMPOTENT CONFIGURATIONS IN SEMISIMPLE ASSOCIATIVE ALGEBRAS

Abstract

This is an introductory survey on the theories of orthogonal decompositions of associative algebras, balanced systems of idempotents, H-bijections of groups and H _R -isomorphisms of group rings. These new theories have grown up from the investigations of orthogonal decompositions of simple Lie algebras into a sum of Cartan subalgebras carried out by A. I. Kostrikin with collaborators.

ACKNOWLEDGMENTS

This work was carried out with the financial support of the Russian Fondation for Basic Research (grant no. 99-01-00233)

Notes

^*In what follows we shall also use abbreviations “OD” or simply “decomposition”.

^*If D is of type 2M₁ then we obtain an Hadamard 3-design.

^*This is the standard abbreviation of “fixed point free”.

^*“GH” abbreviates “generalized Hadamard”.