Lie algebras graded by 3-graded root systems and Jordan pairs covered by grids

American Journal of Mathematics

Volumn 118, Issue 2, 1996, Pages 439-491

  Neher, Erhard ^a  

^a UNIVERSITY OF OTTAWA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038877716     PISSN: 00029327     EISSN: None     Source Type: Journal    
DOI: 10.1353/ajm.1996.0018     Document Type: Article

References (37)

1. S. Berman, Y. Gao, and Y. Krylyuk, Quantum tori and the structure of elliptic quasi-simple Lie algebras, J. Funct. Anal. 135 (1996), 339-389.
2. 2, Trans. Amer. Math. Soc. 347 (1995), 4315-4363.
3. S. Berman and Y. Krylyuk, Universal central extensions of twisted and untwisted Lie algebras extended over commutative rings. J. Algebra 173 (1995), 302-347.
4. S. Berman and V. R. Moody, Lie algebras graded by finite root systems and the intersection matrix algebras by Slodowy, Invent. Math. 108 (1992), 323-347.
5. N. Bourbaki, Groupes et Algèbres de Lie, Hermann, Paris, 1975.
6. _, Groupes et Algèbres de Lie, Masson, Paris, 1981.
7. A. Borel, Linear Algebraic Groups, 2nd ed., Springer-Verlag, New York, 1991.
8. G. Benkart and E. Zelmanov, Lie algebras graded by root systems, Invent. Math. (to appear).
9. J. Faulkner, Barbilian planes, Geom. Dedicata 30 (1989), 125-181.
10. J. Humphreys, Introduction to Lie algebras and Representation Theory, GTM vol. 9, Springer-Verlag, New York, 1972.
11. N. Jacobson, Exceptional Lie Algebras, Lecture Notes in Pure and Appl. Math., vol. 1, Marcel Dekker, New York, 1971.
12. _, Structure Theory of Jordan Algebras, Univ. of Arkansas Lecture Notes in Math., vol. 5, University of Arkansas, Fayetteville, 1981.
13. I. L. Kantor, Classification of irreducible transitive differential groups, Dokl. Akad. Nauk SSSR 158 (1964), 1271-1274.
14. _, Non-linear transformation groups defined by general norms of Jordan algebras, Dokl. Akad. Nauk SSSR 172 (1967), 176-180.
15. _, Some generalizations of Jordan algebras, Trudy Sem. Vektor. Tenzor. Anal. 16 (1972), 407-499 (in Russian).
16. C. Kassel, Kähler differentials and coverings of complex simple Lie algebras extended over a commutative algebra , J. Pure Appl. Algebra 34 (1984), 265-275.
17. C. Kassel and J. L. Loday, Extentions centrales d'algèbres de Lie, Ann. Inst. Fourier 32 (1982), 119-142.
18. M. Koecher, Imbedding of Jordan algebras into Lie algebras I, Amer. J. Math. 89 (1967), 787-816; II, Amer. J. Math. 90 (1968), 476-510.
19. M. Koecher, Imbedding of Jordan algebras into Lie algebras I, Amer. J. Math. 89 (1967), 787-816; II, Amer. J. Math. 90 (1968), 476-510.
20. O. Loos, Jordan Pairs, Lecture Notes in Math., vol. 460, Springer-Verlag, New York, 1975.
21. K. McCrimmon, Alternative Algebras, preprint.
22. K. Meyberg, Lectures on algebras and triple systems, lecture notes, The University of Virginia, Charlottesville, 1972.
23. K. McCrimmon and K. Meyberg, Coordinatization of Jordan triple systems, Comm. Algebra 9 (1981), 1495-1542.
24. K. McCrimmon and E. Neher, Coordinatization of Triangulated Jordan Systems, J. Algebra 114 (1988), 411-451.
25. E. Neher, Jordan Triple Systems by the Grid Approach, Lecture Notes in Math., vol. 1280, Springer-Verlag, New York, 1987
26. _, Systèmes de racines 3-gradués, C. R. Acad. Sci. Paris Sér. I Math. 310 (1990), 687-690.
27. _, 3-graded root systems and grids in Jordan triple systems, J. Algebra 140 (1991), 284-329.
28. _, Generators and relations for 3-graded Lie algebras, J. Algebra 155 (1993), 1-35.
29. _, 3-graded root systems, in preparation.
30. R. D. Schafer, An Introduction to Nonassociative Algebras, Academic Press, New York, 1966.
31. G. B. Seligman, Rational Methods in Lie Algebras, Lecture Notes in Pure and Appl. Math., vol. 17, Marcel Dekker, New York, 1976.
32. P. Slodowy, Singularitäten, Kac-Moody-Liealgebren, assozierte Gruppen und Verallgemeinerungen, Habilitationsschrift, Universität Bonn, 1984.
33. _, Beyond Kac-Moody algebras, and inside, Can. Math. Soc. Conf. Proc. 5 (1986), 361-371.
34. J. Tits, Une classe d'algèbres de Lie en relation avec les algèbres de Jordan, Nederl. Akad. Wetensch. Proc. Ser. A 65 = Indag. Math. 24 (1962), 530-535.
35. _, Classification of algebraic semisimple groups, Proc. Sympos. Pure Math., vol. IX, Amer. Math. Soc., 1966, pp. 33-62.
36. W. L. J. van der Kallen, Infinitesimally Central Extensions of Chevalley Groups, Lecture Notes in Math., vol. 356, Springer-Verlag, New York, 1973.
37. K. A. Zhevlakov, A. M. Slin'ko, I. P. Shestakov, and A. I. Shirshov, Rings that are Nearly Associative, Pure and Appl. Math., vol. 104, Academic Press, Boston, MA, 1982.