ℤ -graded Lie superalgebras of infinite depth and finite growth

Nicoletta Cantarini

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2002)

  • Volume: 1, Issue: 3, page 545-568
  • ISSN: 0391-173X

Abstract

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

How to cite

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Cantarini, Nicoletta. "$\mathbb {Z}$-graded Lie superalgebras of infinite depth and finite growth." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 1.3 (2002): 545-568. <http://eudml.org/doc/84480>.

@article{Cantarini2002,
abstract = {In 1998 Victor Kac classified infinite-dimensional $\mathbb \{Z\}$-graded Lie superalgebras of finite depth. We construct new examples of infinite-dimensional Lie superalgebras with a $\mathbb \{Z\}$-gradation of infinite depth and finite growth and classify $\mathbb \{Z\}$-graded Lie superalgebras of infinite depth and finite growth under suitable hypotheses.},
author = {Cantarini, Nicoletta},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {3},
pages = {545-568},
publisher = {Scuola normale superiore},
title = {$\mathbb \{Z\}$-graded Lie superalgebras of infinite depth and finite growth},
url = {http://eudml.org/doc/84480},
volume = {1},
year = {2002},
}

TY - JOUR
AU - Cantarini, Nicoletta
TI - $\mathbb {Z}$-graded Lie superalgebras of infinite depth and finite growth
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2002
PB - Scuola normale superiore
VL - 1
IS - 3
SP - 545
EP - 568
AB - In 1998 Victor Kac classified infinite-dimensional $\mathbb {Z}$-graded Lie superalgebras of finite depth. We construct new examples of infinite-dimensional Lie superalgebras with a $\mathbb {Z}$-gradation of infinite depth and finite growth and classify $\mathbb {Z}$-graded Lie superalgebras of infinite depth and finite growth under suitable hypotheses.
LA - eng
UR - http://eudml.org/doc/84480
ER -

References

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  1. [H] J. E. Humphreys, “Introduction to Lie Algebras and Representation Theory”, Graduate Texts in Mathematics, 9. Springer-Verlag, New York-Berlin, 1978. Zbl0447.17001MR499562
  2. [K1] V. G. Kac, Simple Irreducible Graded Lie Algebras of Finite Growth, Math. USSR - Izvestija, Vol 2, 6 (1968). Zbl0222.17007MR259961
  3. [K2] V. G. Kac, Lie Superalgebras, Adv. Math. 26 (1977), 8-96. Zbl0366.17012MR486011
  4. [K3] V. G. Kac, Classification of Infinite-Dimensional Simple Linearly Compact Lie Superalgebras, Adv. Math. 139 (1998), 1-55. Zbl0929.17026MR1652530
  5. [K4] V. G. Kac, “Infinite Dimensional Lie Algebras”, Cambridge University Press, Boston, 1990. Zbl0716.17022MR1104219
  6. [M] O. Mathieu, Classification of Simple Graded Lie Algebras of Finite Growth, Invent. Math. 108 (1992), 455-519. Zbl0769.17018MR1163236
  7. [OV] A. L. Onishchik – E. B. Vinberg, “Lie Groups and Algebraic Groups”, Springer-Verlag, New York-Berlin, 1990. Zbl0722.22004MR1064110
  8. [vdL] J. W. van de Leur, A Classification of Contragredient Lie Superalgebras, Comm. Algebra 17 (1989), 1815-1841. Zbl0685.17013MR1013470

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