Geodesic
Nondegeneracy for Lie Triple Systems and Kantor Pairs
Canadian mathematical bulletin, Tome 54 (2011) no. 3, pp. 442-455

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

We study the transfer of nondegeneracy between Lie triple systems and their standard Lie algebra envelopes as well as between Kantor pairs, their associated Lie triple systems, and their Lie algebra envelopes. We also show that simple Kantor pairs and Lie triple systems in characteristic 0 are nondegenerate.
DOI : 10.4153/CMB-2011-023-9
Mots-clés : 17A40, 17B60, 17B99, Kantor pairs, Lie triple systems, Lie algebras 
García, Esther; Lozano, Miguel Gómez; Neher, Erhard. Nondegeneracy for Lie Triple Systems and Kantor Pairs. Canadian mathematical bulletin, Tome 54 (2011) no. 3, pp. 442-455. doi: 10.4153/CMB-2011-023-9
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[1] [1] Allison, B. N. and Faulkner, J. R., Elementary groups and invertibility for Kantor pairs. Comm. Algebra 27(1999), no. 2, 519–556. doi:10.1080/00927879908826447 Google Scholar

[2] [2] Benkart, G. and Smirnov, O., Lie algebras graded by the root system BC . J. Lie Theory 13(2003), no. 1, 91–132. Google Scholar

[3] [3] Martín, A. J. Calderón and Piulestán, M. F., Inheritance of primeness by ideals in Lie triple systems. In: Algebras, rings and their representations, World Sci. Publ., Hackensack, NJ, 2006, pp. 7–16. Google Scholar

[4] [4] López, A. Fernández, García, E., and Lozano, M. Gómez, The Jordan socle and finitary Lie algebras. J. Algebra 280(2004), no. 2, 635–654. Google Scholar

[5] [5] López, A. Fernández, García, E., The Jordan algebras of a Lie algebra. J. Algebra 308(2007), no. 1, 164–177. Google Scholar

[6] [6] García, E. and Lozano, M. Gómez, Jordan systems of Martindale-like quotients. J. Pure Appl. Algebra 194(2004), no. 1–2, 127–145. doi:10.1016/j.jpaa.2004.04.001 Google Scholar

[7] [7] García, E. and Lozano, M. Gómez, An elemental characterization of strong primeness in Lie algebras. J. Algebra 312(2007), no. 1, 132–141. doi:10.1016/j.jalgebra.2006.11.003 Google Scholar

[8] [8] Grishkov, A. N., Local nilpotency of an ideal of a Lie algebra generated by second-order elements. (Russian) Sibirsk. Mat. Zh. 23(1982), no. 1, 181–182, 222. Google Scholar

[9] [9] Jacobson, N., Structure and representations of Jordan algebras. American Mathematical Society Colloquium Publications, XXXIX, American Mathematical Society, Providence, RI, 1968. Google Scholar

[10] [10] Kantor, I. L., Certain generalizations of Jordan algebras. (Russian) Trudy Sem. Vektor. Tenzor. Anal. 16(1972), 407–499. Google Scholar

[11] [11] Kantor, I. L., Models of the exceptional Lie algebras. (Russian) Dokl. Akad. Nauk SSSR 208(1973), 1276–1279. Google Scholar

[12] [12] Lister, W. G., A structure theory of Lie triple systems. Trans. Amer. Math. Soc. 72(1952), 217–242. Google Scholar

[13] [13] Loos, O., Jordan pairs. Lecture Notes in Mathematics, 460, Springer-Verlag, Berlin-New York, 1975. Google Scholar

[14] [14] Meyberg, K., Lectures on algebras and triple systems. Notes on a course of lectures given during the academic year 1971–1972, The University of Virginia, Charlottesville, Va., 1972. Google Scholar

[15] [15] Smirnov, O. N., Simple associative algebras with finite -grading. J. Algebra 196(1997), no. 1, 171–184. doi:10.1006/jabr.1997.7087 Google Scholar

[16] [16] Zel’manov, E. I., Absolute zero-divisors in Jordan pairs and Lie algebras. (Russian) Mat. Sb. (N.S.) 112(154)(1980), no. 4(8), 611–629. Google Scholar

[17] [17] Zel’manov, E. I., Lie algebras with algebraic associated representation. Mat. Sb. (N.S.) 121(163)(1983), no. 4, 545–561. Google Scholar

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