Geodesic
The General Structure of G-Graded Contractions of Lie Algebras I. The Classification
Canadian journal of mathematics, Tome 58 (2006) no. 6, pp. 1291-1340

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

We give the general structure of complex (resp., real) $G$ -graded contractions of Lie algebras where $G$ is an arbitrary finite Abelian group. For this purpose, we introduce a number of concepts, such as pseudobasis, higher-order identities, and sign invariants. We characterize the equivalence classes of $G$ -graded contractions by showing that our set of invariants (support, higher-order identities, and sign invariants) is complete, which yields a classification.
DOI : 10.4153/CJM-2006-046-x
Mots-clés : 17B05, 17B70, Lie algebras, graded contractions 
Weimar-Woods, Evelyn. The General Structure of G-Graded Contractions of Lie Algebras I. The Classification. Canadian journal of mathematics, Tome 58 (2006) no. 6, pp. 1291-1340. doi: 10.4153/CJM-2006-046-x
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[1] [1] Couture, M., Patera, J., Sharp, R. T. and Winternitz, P., Graded contractions of sl(3, ℂ). J. Math. Phys. 32(1991), 2310–2318. Google Scholar

[2] [2] Hussin, A., King, R. C., Leng, X. and Patera, J., Graded contractions of the affine Lie algebra , its representations and tensor products, and an application to the branching rule . J. Phys. A 27(1994), no. 12, 4125–4125. Google Scholar

[3] [3] Inönü, E. and Wigner, E. P., On the contraction of groups and their representations. Proc. Nat. Acad. Sci. U.S.A. 39(1953), 510–524. Google Scholar

[4] [4] de Montigny, M. and Patera, J., Discrete and continuous graded contractions of Lie algebras and superalgebras. J. Phys. A 24(1991) no. 3, 525–547. Google Scholar

[5] [5] de Montigny, M., Patera, J. and Tolar, J., Graded contractions and kinematical groups of space-time. J. Math. Phys. 35(1994), no. 1, 405–425. Google Scholar

[6] [6] Moody, R. V. and Patera, J., Discrete and continuous graded contractions of representations of Lie algebras. J. Phys. A 24(1991) no. 10, 2227–2257. Google Scholar

[7] [7] Patera, J., Pogosyan, G. and Winternitz, P., Graded contractions of the Lie algebra. (2, 1), J. Phys. A 32(1999), 805–826. Google Scholar

[8] [8] Rotman, J. J., The Theory of Groups. An Introduction. Allyn and Bacon, Boston, 1973. Google Scholar

[9] [9] Saletan, E. J., Contractions of Lie groups. J. Math. Phys. 2(1961), 1–21. Google Scholar

[10] [10] Segal, I. E., A class of operator algebras which are determined by groups. Duke Math. J. 18(1951), 221–265. Google Scholar

[11] [11] Tolar, J. and Trávniček, P., Graded contractions and the conformal group of Minkowski space-time. J. Math. Phys. 36(1995), no. 8, 4489–4506. Google Scholar

[12] [12] Tolar, J. and Trávniček, P., Graded contractions of symplectic Lie algebras in collective models, J. Math. Phys. 38(1997) no. 1, 501–523. Google Scholar

[13] [13] Weimar-Woods, E., Contractions of Lie algebras. Generalized Inönü-Wigner contractions versus graded contractions. J. Math. Phys. 36(1995), no. 8, 4519–4548. Google Scholar

[14] [14] Weimar-Woods, E., Contractions, generalized Inönü-Wigner contractions and deformations of finite-dimensional Lie algebras. Rev. Math. Phys. 12(2000), no. 11, 1505–1529. Google Scholar

[15] [15] Weimar-Woods, E., The general structure of G-graded contractions of Lie algebras. II. The contracted Lie algebra. Rev. Math. Phys. 18(2006), no. 6, 655–711. Google Scholar

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