Hom-李color代數(shù)和完美李color代數(shù)的線性變換的若干性質(zhì)
發(fā)布時間：2018-09-07 20:33
【摘要】：本論文的主要內(nèi)容分成兩部分.第一部分研究了特征不等于2的完美李color代數(shù)的兩類線性變換:三導(dǎo)子和三同態(tài),證明了完美李color代數(shù)的三導(dǎo)子都是它的導(dǎo)子,導(dǎo)子代數(shù)的三導(dǎo)子都是它的內(nèi)導(dǎo)子,同時給出了完美李color代數(shù)的一個三同態(tài)是同態(tài)、反同態(tài)、同態(tài)與反同態(tài)的和的必要條件.第二部分研究了Hom-李color代數(shù)的六類線性變換:型心、擬型心、導(dǎo)子、中心導(dǎo)子、擬導(dǎo)子、廣義導(dǎo)子.我們證明了中心導(dǎo)子代數(shù)是導(dǎo)子代數(shù)的Hom-理想,型心是導(dǎo)子代數(shù)的理想,以及一個中心為0的Hom-李color代數(shù)的擬型心是交換的,當且僅當它是一個Hom-李color代數(shù).其次證明了廣義導(dǎo)子代數(shù)等于擬導(dǎo)子代數(shù)和擬型心的和,最后證明了擬導(dǎo)子代數(shù)可以嵌入到一個比它更大的Hom-李color代數(shù)的導(dǎo)子代數(shù)中.
[Abstract]:The main content of this paper is divided into two parts. In the first part, we study two kinds of linear transformations of perfect lie color algebras whose characteristic is not equal to 2: three derivations and three homomorphisms. It is proved that the three derivations of perfect lie color algebras are its derivations, and the three derivations of derivation algebras are its inner derivations. A necessary condition for the sum of homomorphism, anti-homomorphism, homomorphism and anti-homomorphism of a perfect lie color algebra is also given. In the second part, we study six kinds of linear transformations of Hom- lie color algebras: type center, quasi type center, derivation, center derivation, quasi derivation and generalized derivation. We prove that the central derivation algebra is the Hom- ideal of the derivation algebra, the type center is the ideal of the derivation algebra, and the quasi-type center of a Hom- lie color algebra with center 0 is commutative if and only if it is a Hom- lie color algebra. Secondly, it is proved that the generalized derivation algebra is equal to the sum of the quasi derivation algebra and the quasi type center. Finally, it is proved that the quasi derivation algebra can be embedded into the derivation algebra of a Hom- lie color algebra larger than it.
【學位授予單位】：東北師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O152.5
本文編號：2229341
[Abstract]:The main content of this paper is divided into two parts. In the first part, we study two kinds of linear transformations of perfect lie color algebras whose characteristic is not equal to 2: three derivations and three homomorphisms. It is proved that the three derivations of perfect lie color algebras are its derivations, and the three derivations of derivation algebras are its inner derivations. A necessary condition for the sum of homomorphism, anti-homomorphism, homomorphism and anti-homomorphism of a perfect lie color algebra is also given. In the second part, we study six kinds of linear transformations of Hom- lie color algebras: type center, quasi type center, derivation, center derivation, quasi derivation and generalized derivation. We prove that the central derivation algebra is the Hom- ideal of the derivation algebra, the type center is the ideal of the derivation algebra, and the quasi-type center of a Hom- lie color algebra with center 0 is commutative if and only if it is a Hom- lie color algebra. Secondly, it is proved that the generalized derivation algebra is equal to the sum of the quasi derivation algebra and the quasi type center. Finally, it is proved that the quasi derivation algebra can be embedded into the derivation algebra of a Hom- lie color algebra larger than it.
【學位授予單位】：東北師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O152.5
【參考文獻】
相關(guān)期刊論文 前2條
1 陳良云;;Hom-李型代數(shù)的若干結(jié)果[J];四川師范大學學報(自然科學版);2017年02期
2 馬瑤;陳良云;林潔;;李color代數(shù)的T~*-擴張[J];數(shù)學年刊A輯(中文版);2014年05期
，本文編號：2229341
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