M-階化廣義李超代數(shù)H(n)的導(dǎo)子超代數(shù)

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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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)