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Representations Subduced on an Ideal of a Lie Algebra
- Source :
- Canadian Journal of Mathematics. 14:293-303
- Publication Year :
- 1962
- Publisher :
- Canadian Mathematical Society, 1962.
-
Abstract
- This paper considers the properties of the representation of a Lie algebra when restricted to an ideal, the subduced* representation of the ideal. This point of view leads to new forms for irreducible representations of Lie algebras, once the concept of matrices of invariance is developed. This concept permits us to show that irreducible representations of a Lie algebra, over an algebraically closed field, can be expressed as a Lie-Kronecker product whose factors are associated with the representation subduced on an ideal. Conversely, if one has such factors, it is shown that they can be put together to give an irreducible representation of the Lie algebra. A valuable guide to this work was supplied by a paper of Clifford (1).
- Subjects :
- General Mathematics
010102 general mathematics
Universal enveloping algebra
Lie superalgebra
01 natural sciences
Affine Lie algebra
Super-Poincaré algebra
Lie conformal algebra
Graded Lie algebra
Algebra
0103 physical sciences
Algebra representation
Fundamental representation
010307 mathematical physics
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 14964279 and 0008414X
- Volume :
- 14
- Database :
- OpenAIRE
- Journal :
- Canadian Journal of Mathematics
- Accession number :
- edsair.doi...........6de4431c81f0d7f5aff55759c3c06792