Hostname: page-component-cb9f654ff-9b74x Total loading time: 0 Render date: 2025-08-26T22:54:02.961Z Has data issue: false hasContentIssue false
  • English
  • Français

Quasi Clifford algebras and systems of orthogonal designs

Part of: Basic linear algebra Designs and configurations

Published online by Cambridge University Press:  09 April 2009

H. M. Gastineau-Hills
H. M. Gastineau-Hills
Affiliation:
Department of Mathematics, University of Sydney, Sydney, NSW 2006, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The representation theory of Clifford algebras has been used to obtain information on the possible orders of amicable pairs of orthogonal designs on given numbers of variables. If, however, the same approach is tried on more complex systems of orthogonal designs, such as product designs and amicable triples, algebras which properly generalize the Clifford algebras are encountered. In this paper a theory of such generalizations is developed and applied to the theory of systems of orthogonal designs, and in particular to the theory of product designs.

MSC classification

Secondary: 15A66: Clifford algebras, spinors 05B15: Orthogonal arrays, Latin squares, Room squares

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 32 , Issue 1 , January 1982 , pp. 1 - 23
Copyright
Copyright © Australian Mathematical Society 1982

References

[1] Albert, A. A., Structure of algebras (American Mathematical Society Colloquium Publication, Vol. XXIV, 1939).Google Scholar
[2] Artin, E., Geometric algebra (Interscience Tracts in Pure and Applied Mathematics No. 3, 1957).Google Scholar
[3] Burrow, M., Representation theory of finite groups (Academic Press New York and London, 1965).Google Scholar
[4] Curtis, C. W. and Reiner, I., Representation theory of finite groups and associative algebras (Pure and Applied Mathematics, Vol. XI, Interscience Publishers, John Wiley and Sons, 1962).Google Scholar
[5] Gastineau-Hills, H. M., Systems of orthogonal designs and quasi Clifford algebras (Ph. D. Thesis, University of Sydney, to appear.)Google Scholar
[6] Geramita, A. and Seberry, J., Orthogonal designs: quadratic forms and Hadamard matrices (Marcel Dekker, New York, 1979).Google Scholar
[7] Kawada, Y. and Iwahori, N., ‘On the structure and representations of Clifford algebras’, J. Math. Soc. Japan 2 (1950), 34–43.Google Scholar
[8] Robinson, P. J., ‘Using product designs to construct orthogonal designs’, Bull. Austral Math. Soc. 16 (1977), 297–305.CrossRefGoogle Scholar
[9] Wolfe, W. W., Orthogonal designs-amicable orthogonal designs (Ph. D. Thesis, Queen's University Kingston, Ontario, Canada, 1975).Google Scholar