-graded Lie superalgebras of infinite depth and finite growth
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 1 (2002) no. 3, p. 545-568

In 1998 Victor Kac classified infinite-dimensional -graded Lie superalgebras of finite depth. We construct new examples of infinite-dimensional Lie superalgebras with a -gradation of infinite depth and finite growth and classify -graded Lie superalgebras of infinite depth and finite growth under suitable hypotheses.

Classification:  17B65,  17B70
@article{ASNSP_2002_5_1_3_545_0,
     author = {Cantarini, Nicoletta},
     title = {$\mathbb {Z}$-graded Lie superalgebras of infinite depth and finite growth},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 1},
     number = {3},
     year = {2002},
     pages = {545-568},
     zbl = {1097.17014},
     mrnumber = {1990672},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2002_5_1_3_545_0}
}
Cantarini, Nicoletta. $\mathbb {Z}$-graded Lie superalgebras of infinite depth and finite growth. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 1 (2002) no. 3, pp. 545-568. http://www.numdam.org/item/ASNSP_2002_5_1_3_545_0/

[H] J. E. Humphreys, “Introduction to Lie Algebras and Representation Theory”, Graduate Texts in Mathematics, 9. Springer-Verlag, New York-Berlin, 1978. | MR 499562 | Zbl 0447.17001

[K1] V. G. Kac, Simple Irreducible Graded Lie Algebras of Finite Growth, Math. USSR - Izvestija, Vol 2, 6 (1968). | MR 259961 | Zbl 0222.17007

[K2] V. G. Kac, Lie Superalgebras, Adv. Math. 26 (1977), 8-96. | MR 486011 | Zbl 0366.17012

[K3] V. G. Kac, Classification of Infinite-Dimensional Simple Linearly Compact Lie Superalgebras, Adv. Math. 139 (1998), 1-55. | MR 1652530 | Zbl 0929.17026

[K4] V. G. Kac, “Infinite Dimensional Lie Algebras”, Cambridge University Press, Boston, 1990. | MR 1104219 | Zbl 0716.17022

[M] O. Mathieu, Classification of Simple Graded Lie Algebras of Finite Growth, Invent. Math. 108 (1992), 455-519. | MR 1163236 | Zbl 0769.17018

[OV] A. L. Onishchik - E. B. Vinberg, “Lie Groups and Algebraic Groups”, Springer-Verlag, New York-Berlin, 1990. | MR 1064110 | Zbl 0722.22004

[vdL] J. W. Van De Leur, A Classification of Contragredient Lie Superalgebras, Comm. Algebra 17 (1989), 1815-1841. | MR 1013470 | Zbl 0685.17013