馬麗麗,張永正

(1.齊齊哈爾大學(xué)理學(xué)院,黑龍江齊齊哈爾 161006; 2.東北師范大學(xué)數(shù)學(xué)與統(tǒng)計學(xué)院,吉林長春 130024)

M-階化廣義李超代數(shù)H(n)的導(dǎo)子超代數(shù)

馬麗麗1,張永正2

(1.齊齊哈爾大學(xué)理學(xué)院,黑龍江齊齊哈爾 161006; 2.東北師范大學(xué)數(shù)學(xué)與統(tǒng)計學(xué)院,吉林長春 130024)

給出了M-階化廣義李超代數(shù)H(n)的定義,證明了M-階化廣義李超代數(shù)H(n)是Z-階化的,刻畫了H(n)的導(dǎo)子超代數(shù)的Z-階化成分,進(jìn)而確定了M-階化廣義李超代數(shù)H(n)的導(dǎo)子超代數(shù).

M-階化;廣義李超代數(shù);導(dǎo)子超代數(shù)

1 預(yù)備知識

2 主要結(jié)果及其證明

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[2] WANG Y D,ZHANG Y Z.Generalized Lie superalgebras of cartan-type[J].Journal of Mathematical Research Exposition, 1995,15:85-90.

[3] ZHANG Y Z.Finite-dimensional Lie superalgebras of Caran-type over fields of p rime characteristic[J].Chinese Science Bulletin,1997,42(9):720-724.

[4] ZHANGQ C,ZHANG Y Z.Derivation algebras of themodular Lie superalgebrasWandSof Cartan-type[J].Acta Math Sci, 2000,20(1):137-144.

[5] WANG Y,ZHANG Y Z.Derivation algebra Der(H)and central extensions of Lie superalgebras[J].Commun A lgebra,2004, 32:4117-4131.

[6] MA FM,ZHANGQ C.Derivation algebra of modular Lie superalgebraKof Cartan-type[J].J Math,2000,20(4):431-435.

[7] 吳險峰.低維李超三系的分類[J].吉林大學(xué)學(xué)報:理學(xué)報,2009,47(4):671-676.

[8] STRADE H,FARNSTEINER R.Modular Lie algebrasand their rep resentations[M].New York:Marcel Dekker Inc,1988:118-140.

[9] 張永正,劉文德.模李超代數(shù)[M].北京:科學(xué)出版社,2004:48-62.

The derivation superalgebra of M-graded generalized L ie superalgebra H(n)

MA Li-li1,ZHANG Yong-zheng2

(1.School of Science,Qiqihar University,Qiqihar 161006,China; 2.School of Mathematics and Statistics,Northeast Normal University,Changchun 130024,China)

In this paper,first defineM-graded generalized Lie superalgebraH(n),and p rove thatM-graded generalized Lie superalgebraH(n)isZ-graded,then describe theZ-graded elements of derivation superalgebra ofH(n).Furthermo re,the derivation superalgebra ofM-graded generalized Lie superalgebraH(n)is determined.

M-graded;generalized Lie superalgebra;derivation superalgebra

O 152.5

110·21

A

1000-1832(2010)04-0006-06

2010-03-04

國家自然科學(xué)基金資助項目(10871057).

馬麗麗(1979—),女,碩士,講師,主要從事李代數(shù)與李超代數(shù)研究;通訊作者:張永正(1947—),男,博士,教授,博士研究生導(dǎo)師,主要從事李代數(shù)與李超代數(shù)研究.

(責(zé)任編輯:陶 理)