In this paper,we give the definition of a c-ideal of a Lie superalgebra and get some propositions of them.By these propositions,we study the solvability and supersolvability of Lie superalgebras.We prove that a Lie su...In this paper,we give the definition of a c-ideal of a Lie superalgebra and get some propositions of them.By these propositions,we study the solvability and supersolvability of Lie superalgebras.We prove that a Lie superalgebra L is solvable if and only if all maximal subalgebras of L are c-ideals of L.We also obtain some conditions for supersolvability of a Lie superalgebra.展开更多
The main purpose of the present paper is to give some properties of the Jacobson radical, the Frattini subsystem and c-ideals of a Lie triple system. Some further results concerning the Frattini subsystems of nilpoten...The main purpose of the present paper is to give some properties of the Jacobson radical, the Frattini subsystem and c-ideals of a Lie triple system. Some further results concerning the Frattini subsystems of nilpotent and solvable Lie triple systems are obtained. Moreover, we develop inititally c-ideals for a Lie triple system and make use of them to give some characterizations of a solvable Lie triple system.展开更多
基金Supported by Major Research Project of Yili Normal University(No.2024YSZD008)NNSF of China(Nos.11771069 and 12071405).
文摘In this paper,we give the definition of a c-ideal of a Lie superalgebra and get some propositions of them.By these propositions,we study the solvability and supersolvability of Lie superalgebras.We prove that a Lie superalgebra L is solvable if and only if all maximal subalgebras of L are c-ideals of L.We also obtain some conditions for supersolvability of a Lie superalgebra.
基金the National Natural Science Foundation of China(Nos.11171055,11071068,11126129)the Natural Science Foundation of Jilin Province(No.201115006)+4 种基金the Scientific ResearchFoundation for Returned Scholars Ministry of Education of Chinathe Natural Science Foundationof Zhejiang Province(No.D7080080)Qianjiang Excellence Project(No.2007R10031)the InnovationTeam Foundation of the Department of Education of Zhejiang Province(No.T200924)the PhDStart-up Foundation of Liaoning University of China(No.2012002)
文摘The main purpose of the present paper is to give some properties of the Jacobson radical, the Frattini subsystem and c-ideals of a Lie triple system. Some further results concerning the Frattini subsystems of nilpotent and solvable Lie triple systems are obtained. Moreover, we develop inititally c-ideals for a Lie triple system and make use of them to give some characterizations of a solvable Lie triple system.
