Derivations of the even parts into the odd parts of the odd Hamiltonian Lie superalgebras

HUA Xiu-ying; LIU Wen-de

Issue 4

Jul. 2014

Turn off MathJax

Article Contents

Article Navigation > Journal of East China Normal University (Natural Sciences) > 2014 > (4): 1-7

HUA Xiu-ying, LIU Wen-de. Derivations of the even parts into the odd parts of the odd Hamiltonian Lie superalgebras[J]. Journal of East China Normal University (Natural Sciences), 2014, (4): 1-7.

Citation:

HUA Xiu-ying, LIU Wen-de. Derivations of the even parts into the odd parts of the odd Hamiltonian Lie superalgebras[J]. Journal of East China Normal University (Natural Sciences), 2014, (4): 1-7.

HUA Xiu-ying, LIU Wen-de. Derivations of the even parts into the odd parts of the odd Hamiltonian Lie superalgebras[J]. Journal of East China Normal University (Natural Sciences), 2014, (4): 1-7.

Citation:

HUA Xiu-ying, LIU Wen-de. Derivations of the even parts into the odd parts of the odd Hamiltonian Lie superalgebras[J]. Journal of East China Normal University (Natural Sciences), 2014, (4): 1-7.

PDF( 245 KB)

Derivations of the even parts into the odd parts of the odd Hamiltonian Lie superalgebras

HUA Xiu-ying¹,
LIU Wen-de²

1.
School of Applied Sciences, Harbin University of Science and Technology, Harbin 150080, China;
2.
School of Mathematical Sciences, Harbin Normal University, Harbin 150025, China

Received Date: 2013-07-01
Rev Recd Date: 2013-10-01
Publish Date: 2014-07-25

Abstract

Abstract

For the problem of the derivations of the even part into the odd part of the finite-dimensional odd Hamiltonian superalgebras over a field of characteristic $p3,$ by using the generating set of the even part and calculating the action of derivations on its generating set, the nonnegative $\mathbb{Z}$-homogeneous derivations of the even part into the odd part were determined. Furthermore, by applying the properties of the even part, the negative $\mathbb{Z}$-homogeneous derivations of the even part into the odd part were given. Therefore, all derivations of the even part into the odd part of the finite-dimensional odd Hamiltonian superalgebras were characterized, which has important significance to further study the structure, the representation and the classification of Lie superalgebras.
- divided power algebra,
- derivation,
- odd Hamiltonian superalgebra

FullText(HTML)

References(1)

References

[1]

1} KAC V G. Lie superalgebras[J]. Adv Math, 1977, 26(1): 8-96.
{2} KAC V G. Classification of infinite-dimensional simple linearly compact Lie superalgebras[J]. Adv Math, 1998, 139: 1-55.
{3} SUN H Z, HAN Q Z. A survey of Lie superalgebras[J]. Adv Phys (PRC), 1983, 1: 81-125 (in Chinese).
{4} PETROGRADSKI V M. Identities in the enveloping algebras for modular Lie superalgebras[J]. J Algebra, 1992, 145: 1-21.
{5} CELOUSOV M J. Derivations of Lie algebras of Cartan-type[J]. Izv Vyssh Uchebn Zaved Mat, 1970, 98: 126-134 (in Russian).
{6} STRADE H, FARNSTEINER R. Modular Lie algebras and their representations[M]. Monogr Texbooks Pure Appl Math 116. New York: Dekker, 1988: 99-138.
{7} STRADE H. Simple Lie algebras over fields of positive characteristic: I Structure theory[M]. Berlin: Walter de Gruyter, 2004: 184-199.
{8} ZHANG Q C, ZHANG Y Z. Derivation algebras of modular Lie superalgebras W and S of Cartan-type[J]. Acta Math Sci, 2000, 20(1): 137-144.

Relative Articles

Supplements(0)

Cited By

Proportional views