Hostname: page-component-7dd5485656-tbj44 Total loading time: 0 Render date: 2025-10-31T00:22:31.822Z Has data issue: false hasContentIssue false
  • English
  • Français

THE GENERALIZED WITT MODULAR LIE SUPERALGEBRA OF CARTAN TYPE

Part of: Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  18 November 2011

YAN-QIN DONG ,
YONG-ZHENG ZHANG  and
ANGELO EBONZO
YAN-QIN DONG*
Affiliation:
School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, Jilin, PR China Aviation University of Air Force, Changchun 130022, Jilin, PR China (email: dongyq384@nenu.edu.cn)
YONG-ZHENG ZHANG
Affiliation:
School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, Jilin, PR China (email: zhyz@nenu.edu.cn)
ANGELO EBONZO
Affiliation:
Transportation Management College, Dalian Maritime University, Dalian 116026, PR China (email: angedan2000@yahoo.fr)
*
✉For correspondence; e-mail: dongyq384@nenu.edu.cn
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We construct the generalized Witt modular Lie superalgebra of Cartan type. We give a set of generators for and show that is an extension of a subalgebra of by an ideal . Finally, we describe the homogeneous derivations of Z-degree of and we determine the derivation superalgebra of .

Keywords

modular Lie superalgebrasZ-graded Lie superalgebrasderivation superalgebras

MSC classification

Secondary: 17B50: Modular Lie (super)algebras

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 91 , Issue 2 , October 2011 , pp. 145 - 162
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

This work was supported by National Science Foundation of China Funded Projects (Nos. 10871057 and 10701019).

References

[1]Celousov, M. J., ‘Derivations of Lie algebras of Cartan-type’, Izv. Vyssh. Uchebn. Zaved. Mat. 98 (1970), 126–134 (in Russian).Google Scholar
[2]Farnsteiner, R., ‘Note on Frobenius extensions and restricted Lie superalgebras’, J. Pure Appl. Algebra 108 (1996), 241–256.CrossRefGoogle Scholar
[3]Fu, J.-Y., Zhang, Q.-C. and Jiang, C.-B., ‘The Cartan type modular Lie superalgebras KO’, Comm. Algebra 34 (2006), 129–142.CrossRefGoogle Scholar
[4]Kac, V. G., ‘Lie superalgebras’, Adv. Math. 98 (1977), 8–96.CrossRefGoogle Scholar
[5]Kac, V. G., ‘Classification of infinite-dimensional simple linearly compact Lie superalgebras’, Adv. Math. 139 (1998), 1–55.CrossRefGoogle Scholar
[6]Kochetkov, Yu. and Leites, D., ‘Simple Lie algebras in characteristic 2 recovered from superalgebras and on the notion of a simple finite group’, Contemp. Math. 131 (1992), 59–67.CrossRefGoogle Scholar
[7]Liu, W.-D., Zhang, Y.-Z. and Wang, X.-L., ‘The derivation algebra of the Cartan type Lie superalgebras HO’, J. Algebra 273 (2004), 176–205.CrossRefGoogle Scholar
[8]Ma, F.-M. and Zhang, Q.-C., ‘Derivation algebra of modular Lie superalgebra K of Cartan type’, J. Math. (Wuhan) 20 (2000), 431–435.Google Scholar
[9]Petrogradski, V. M., ‘Identities in the enveloping algebras for modular Lie superalgebras’, J. Algebra 145 (1992), 1–21.CrossRefGoogle Scholar
[10]Scheunert, M., Theory of Lie Superalgebras, Lecture Notes in Mathematics, 716 (Springer, New York, 1979).CrossRefGoogle Scholar
[11]Strade, H. and Farnsteiner, R., Modular Lie Algebras and Their Representations, Monographs and Textbooks in Pure and Applied Mathematics, 116 (Marcel Dekker, New York, 1988).Google Scholar
[12]Wang, Y. and Zhang, Y.-Z., ‘Derivation algebra Der( H) and central extensions of Lie superalgebra’, Comm. Algebra 32 (2004), 4117–4131.CrossRefGoogle Scholar
[13]Zhang, Y.-Z., ‘Finite-dimensional Lie superalgebras of Cartan-type over fields of prime characteristic’, Chinese Sci. Bull. 42 (1997), 720–724.CrossRefGoogle Scholar
[14]Zhang, Y.-Z. and Liu, W.-D., Modular Lie Superalgebras (Science Press, Beijing, 2004), (in Chinese).Google Scholar
[15]Zhang, Q.-C. and Zhang, Y.-Z., ‘Derivation algebra of modular Lie superalgebras W and S of Cartan type’, Acta Math. Sci. 20 (2000), 137–144.CrossRefGoogle Scholar