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Generalized Matrix Algebras

Published online by Cambridge University Press:  20 November 2018

W. P. Brown
W. P. Brown*
Affiliation:
King's College, Aberdeen
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The algebras considered here arose in the investigation of an algebra connected with the orthogonal group. We consider an algebra of dimension mn over a field K of characteristic zero, and possessing a basis {eij} (1 ≤ i ≤ m; 1 ≤ j ≤ n) with the multiplication property

1,

The field elements ϕij form a matrix Φ = (ϕij) of order n × m. It will be called the multiplication matrix of the algebra relative to the basis {ϕij}.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 7 , 1955 , pp. 188 - 190
Copyright
Copyright © Canadian Mathematical Society 1955

References

1. Brauer, R., On algebras which are connected with the semisimple continuous groups, Ann. Math., 38 (1937), 857.Google Scholar
2. Weyl, H., The classical groups (Princeton, 1946).Google Scholar