Representations of an exceptional Jordan superalgebra. (English. Russian original) Zbl 0636.17011
Funct. Anal. Appl. 21, No. 1-3, 253-254 (1987); translation from Funkts. Anal. Prilozh. 21, No. 3, 93-94 (1987).
The author gives a description of bimodules over the simple exceptional Jordan superalgebra \(F_{10}\), which was introduced by V. G. Kac [Commun. Algebra 5, 1375–1400 (1977; Zbl 0367.17007)]. Lie superalgebras associated with \(F_{10}\) are also described.
Reviewer: Sh. A. Ayupov (Tashkent)
MSC:
| 17C70 | Super structures |
| 17C10 | Structure theory for Jordan algebras |
| 17C40 | Exceptional Jordan structures |
| 17B10 | Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) |
Citations:
Zbl 0367.17007References:
| [1] | V. G. Kac, Commun. Alg.,5, No. 13, 1375–1400 (1977). · Zbl 0367.17007 · doi:10.1080/00927877708822224 |
| [2] | V. G. Kac, Adv. Math.,26, No. 1, 8–96 (1977). · Zbl 0366.17012 · doi:10.1016/0001-8708(77)90017-2 |
| [3] | I. L. Kantor, in: Proceedings of the Seminar in Vector and Tensor Analysis, No. 13 [in Russian], Moscow State Univ. (1966), pp. 310–398. |
| [4] | L. Hogben and V. G. Kac, Commun. Alg.,11, No. 10, 1155–1156 (1983). |
| [5] | E. I. Zel’manov, Mat. Sb.,121, No. 4, 537–552 (1983). |
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