Geodesic
λ-Mappings Between Representation Rings of Lie Algebras
Canadian journal of mathematics, Tome 35 (1983) no. 5, pp. 898-960

Voir la notice de l'article provenant de la source Cambridge University Press

In [10] Patera and Sharp conceived a new relation, subjoining, between semisimple Lie algebras. Our objective in this paper is twofold. Firstly, to lay down a mathematical formalization of this concept for arbitrary Lie algebras. Secondly, to give a complete classification of all maximal subjoinings between Lie algebras of the same rank, of which many examples were already known to the above authors.The notion of subjoining is a generalization of the subalgebra relation between Lie algebras. To give an intuitive idea of what is involved we take a simple example. Suppose is a complex simple Lie algebra of type B 2. Let be a Cartan subalgebra of and Δ the corresponding root system. We have the standard root diagram Inside B 2 there lies the subalgebra A 1 × A 1 which can be identified with the sum of and the root spaces corresponding to the long roots of B 2. 
Moody, R. V.; Pianzola, A. λ-Mappings Between Representation Rings of Lie Algebras. Canadian journal of mathematics, Tome 35 (1983) no. 5, pp. 898-960. doi: 10.4153/CJM-1983-051-x
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[1] 1. A., Borel and J., de Siebenthal, Les sous-groupes fermés de rang maximum des groupes de Lie clos, Comment. Math. Helv. 23 (1949), 200–221. Google Scholar

[2] 2. N., Bourbaki, Commutative algebra (Addison-Wesley, 1972). Google Scholar

[3] 3. N., Bourbaki, Groupes et algèbres de Lie, Ch. 4, 5, 6 (Hermann, Paris, 1968). Google Scholar

[4] 4. N., Bourbaki, Groupes et algèbres de Lie, Ch. 7, 8 (Hermann, Paris, 1975). Google Scholar

[5] 5. A., Grothendieck, La théorie des classes de Chern, Bull. Soc. Math. France 86 (1958), 137–154. Google Scholar

[6] 6. R. C., King, Unitary group subjoining, J. Phys. A:Math. Gen. 13 (1980). Google Scholar

[7] 7. D., Knutson, X-rings and the representation of the unitary group, Lecture Notes in Mathematics 308 (Springer-Verlag). Google Scholar

[8] 8. S., Lang, Algebraic number theory (Addison-Wesley, 1970). Google Scholar

[9] 9. R. V., Moody, Lie algebra subjoining, C. R. Math. Rep. Acad. Sci. Canada 5 (1980), 259–264. Google Scholar

[10] 10. J., Patera and R., Sharp, Generating functions for plethysms of finite and continuous groups, J. Phys. A:Math. Gen. 13 (1980), 397–416. Google Scholar

[11] 11. J., Patera, R., Sharp and R., Slansky, On a new relation between semi-simple Lie algebras, J. Math. Phys. 21 (1980), 2335. Google Scholar

[12] 12. A., Pianzola, Isomorphically representable Lie algebras, (Thesis), University of Saskatchewan, (1981). Google Scholar

[13] 13. J. F., Adams and Z., Mahmud, Maps between classifying spaces, Inventiones Math. 35 (1976), 1–41. Google Scholar

[14] 14. J. F., Adams, Maps between classifying spaces. II, Inventiones Math. 49 (1978), 1–65. Google Scholar

[15] 15. E. M., Friedlander, Exceptional isogenics and the classifying spaces of simple Lie groups, Ann. Math 101 (1975), 510–520. Google Scholar

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