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Irreducible Representations of Algebras

Published online by Cambridge University Press:  20 November 2018

Edgar G. Goodaire
Edgar G. Goodaire*
Affiliation:
University of British Columbia, Vancouver, British Columbia; Memorial University of Newfoundland, St. John's, Newfoundland
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The concept of the universal enveloping algebra of a (not necessarily associative) algebra X is basic to the study of the representations of X, because there is a one-to-one correspondence between the representations of X and . If one is only interested in studying a certain class of the representations of X, the thought occurs that there may exist a more suitable universal object.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 5 , October 1974 , pp. 1118 - 1129
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Albert, A. A., A structure theory for Jordan algebras, Ann. of Math. 48 (1947), 546–567.Google Scholar
2. Foster, D. M., On Cartan subalgebras of alternative algebras, Trans. Amer. Math. Soc. 162 (1971), 225–238.Google Scholar
3. Herstein, I. N., Noncommutative rings , Cams Mathematical Monographs, Math. Assoc, of Amer. (Wiley, New York, 1968).Google Scholar
4. Jacobson, N., Lie algebras (Wiley (Interscience), New York, 1962).Google Scholar
5. Jacobson, N., Cartan subalgebras of Jordan algebras, Nagoya Math. J. 27 (1966), 591–609.Google Scholar
6. Jacobson, N., Jordan algebras, Coll. Pub. 39 (Amer. Math. Soc, Providence, R.I., 1968).Google Scholar
7. Lemire, F. W., Weight spaces and irreducible representations of simple Lie algebras, Proc. Amer. Math. Soc. 22 (1969), 192–197.Google Scholar