3-Graded Lie Algebras with Jordan Finiteness Conditions

References

• Baranov , A. A. 1999 . Finitary simple Lie algebras . J. Algebra , 219 : 299 – 329 .
   Google Scholar
• Benkart , G. 1977 . On inner ideals and ad-nilpotent elements of Lie algebras . Trans. Am. Math. Soc. , 232 : 61 – 81 .
   Google Scholar
• De La Harpe , P. 1972 . Classical Banach Lie Algebras and Banach Lie Groups in Hilbert Space , Lecture Notes in Mathematics, Vol. 285 New York : Springer-Verlag .
   Google Scholar
• Fernández López , A. and Tocón , M. 2003 . Strongly prime Jordan pairs with non-zero socle . Manuscripta Math , 111 : 321 – 340 .
   Google Scholar
• Fernández López , A. , García , E. and Gómez Lozano , M. The Jordan socle and finitary Lie algebras . J. Algebra , To appear
   Google Scholar
• García , E. 2003a . Inheritance of primeness by ideals in Lie algebras . Int. J. Math. Game Theory Algebra ,
   Google Scholar
• García , E. 2003b . Tits–Kantor–Koecher algebras of strongly prime Hermitian Jordan pairs . Comm. Algebra ,
   Google Scholar
• García , E. Simple, primitive and strongly prime Jordan 3-graded Lie algebras . Comm. Algebra , To appear
   Google Scholar
• García , E. and Neher , E. 2003 . Tits–Kantor–Koecher superalgebras of Jordan superpairs covered by grids . Comm. Algebra , 31 ( 7 ) : 3335 – 3375 .
   Google Scholar
• Jacobson , N. 1962 . Lie Algebras New York : Interscience Publishers .
   Google Scholar
• Jacobson , N. 1968 . Structure of Rings 37 Providence , , USA : AMS Colloquium Publications .
   Google Scholar
• Jacobson , N. 1981 . Structure Theory of Jordan Algebras , Lecture Notes in Mathematics 5 Fayetteville : University of Arkansas .
   Google Scholar
• Kantor , I. L. 1964 . Classification of irreducible transitive differential groups . Dokl. Akad. Nauk SSSR , 158 : 1271 – 1274 .
   Google Scholar
• Kantor , I. L. 1967 . Non-linear transformation groups defined by general norms of Jordan algebras . Dokl. Akad. Nauk SSSR , 172 : 176 – 180 .
   Google Scholar
• Kantor , I. L. 1972 . Some generalizations of Jordan algebras . Trudy Sem. Velktor. Tenzor. Anal. , 16 : 407 – 499 .
   Google Scholar
• Kaplansky , I. 1974 . Linear Algebra and Geometry (A Second Course) New York : Chelsea Publishing Company .
   Google Scholar
• Koecher , M. 1967 . Imbedding of Jordan algebras into Lie algebras I . Am. J. Math. , 89 : 787 – 816 .
   Google Scholar
• Koecher , M. 1968 . Imbedding of Jordan algebras into Lie algebras II . Am. J. Math. , 90 : 476 – 510 .
   Google Scholar
• Loos , O. 1975 . Jordan Pairs , Lecture Notes in Mathematics 460 New York : Springer-Verlag .
   Google Scholar
• Loos , O. 1989 . On the socle of a Jordan pair . Collect. Math. , 40 ( 2 ) : 109 – 125 .
   Google Scholar
• Martínez , C. 2001 . The ring of fractions of a Jordan algebra . J. Algebra , 237 : 798 – 812 .
   Google Scholar
• McCrimmon , K. 1984 . Strong prime inheritance in Jordan systems . Algebras, Groups and Geom. , 1 : 217 – 234 .
   Google Scholar
• Neher , E. 1996 . Lie algebras graded by 3-graded root systems and Jordan pairs covered by grids . Am. J. Math. , 118 ( 2 ) : 439 – 491 .
   Google Scholar
• Strašek , R. and Zalar , B. 2002 . Uniform primeness of classical Banach Lie algebras of compact operators . Publ. Math. Debrecen , 61 ( 3–4 ) : 325 – 340 .
   Google Scholar
• Tits , J. 1962 . Une classe d'algèbres de Lie en relation avec les algèbres de Jordan . Indag. Math. , 24 : 530 – 535 .
   Google Scholar
• Zelmanov , E. I. 1984 . Lie algebras with an algebraic adjoint representation . Math. USSR Sbornik , 49 ( 2 ) : 537 – 552 .
   Google Scholar
• Zelmanov , E. I. 1985 . Lie algebras with a finite grading . Math. USSR Sbornik , 52 ( 2 ) : 537 – 552 .
   Google Scholar
• #Communicated by B. Allison.
   Google Scholar