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Lie Superalgebras Graded by the Root Systems C(n), D(m, n), D(2, 1, α), F(4), G(3)

Published online by Cambridge University Press:  20 November 2018

Georgia Benkart  and
Alberto Elduque
Georgia Benkart
Affiliation:
Department of Mathematics University of Wisconsin Madison, Wisconsin 53706 USA, e-mail: [email protected]
Alberto Elduque
Affiliation:
Departamento de Matemáticas Universidad de Zaragoza 50009 Zaragoza Spain, e-mail: [email protected]
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Abstract

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We determine the Lie superalgebras that are graded by the root systems of the basic classical simple Lie superalgebras of type $C\left( n \right),D\left( m,n \right),D\left( 2,1;\alpha \right)\left( \alpha \in \mathbb{F}\backslash \left\{ 0,-1 \right\} \right),F(4)$, and $G(3)$.

Keywords

17A70
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 4 , 01 December 2002 , pp. 509 - 524
Copyright
Copyright © Canadian Mathematical Society 2002

References

[AABGP] Allison, B. N., Azam, S., Berman, S., Gao, Y. and Pianzola, A., Extended Affine Lie Algebras and Their Root Systems. Mem. Amer.Math. Soc. (126) 603(1997).Google Scholar
[ABG1] Allison, B. N., Benkart, G., Gao, Y., Central extensions of Lie algebras graded by finite root systems. Math. Ann. 316 (2000), 499–527.Google Scholar
[ABG2] Allison, B. N., Benkart, G. and Gao, Y., Lie Algebras Graded by the Root Systems BCr , r ≥ 2. Mem. Amer.Math. Soc. (158) 751 Providence, R.I., 2002.Google Scholar
[BE1] Benkart, G. and Elduque, A., Lie superalgebras graded by the root system B(m, n). Submitted, Jordan preprint archive: http://mathematik.uibk.ac.at/jordan/ (paper 108).Google Scholar
[BE2] Benkart, G. and Elduque, A., Lie superalgebras graded by the root system A(m, n). Submitted, Jordan preprint archive: http://mathematik.uibk.ac.at/jordan/ (paper 124).Google Scholar
[BS] Benkart, G. and Smirnov, O., Lie algebras graded by the root system BC1 . J. Lie Theory, to appear.Google Scholar
[BZ] Benkart, G. and Zelmanov, E., Lie algebras graded by finite root systems and intersection matrix algebras. Invent.Math. 126 (1996), 1–45.Google Scholar
[BM] Berman, S. and Moody, R. V., Lie algebras graded by finite root systems and the intersection matrix algebras of Slodowy. Invent.Math. 108 (1992), 323–347.Google Scholar
[B] Bourbaki, N., Groupes et Algèbres de Lie. Élements de Mathématique XXXIV, Hermann, Paris, 1968.Google Scholar
[GN] García, E. and Neher, E., Jordan superpairs covered by grids and their Tits-Kantor-Koecher superalgebras. preprint, 2001.Google Scholar
[IK] Iohara, K. and Koga, Y., Central extensions of Lie superalgebras. Comment. Math. Helv. 76 (2001), 110–154.Google Scholar
[K1] Kac, V. G., Lie superalgebras. Adv. in Math. 26 (1977), 8–96.Google Scholar
[K2] Kac, V. G., Representations of classical superalgebras. Differential and Geometrical Methods in Math. Physics II, Lecture Notes in Math. 676, Springer-Verlag, Berlin, Heidelberg, New York, 1978, 599–626.Google Scholar
[LS] Lee Shader, C., Typical representations for orthosymplectic Lie superalgebras. Comm. Algebra 28 (2000), 387–400.Google Scholar
[N] Neher, E., Lie algebras graded by 3-graded root systems. Amer. J. Math. 118 (1996), 439–491.Google Scholar
[S] Slodowy, P., Beyond Kac-Moody algebras and inside. Lie Algebras and Related Topics, Canad. Math. Soc. Conf. Proc. 5, (eds., Britten, Lemire, Moody), 1986, 361–371.Google Scholar