The authors first give a necessary and sufficient condition for some solvable Lie algebras with l-step nilpotent radicals to be complete, and then construct a new class of infinite dimensional complete Lie algebras by...The authors first give a necessary and sufficient condition for some solvable Lie algebras with l-step nilpotent radicals to be complete, and then construct a new class of infinite dimensional complete Lie algebras by using the modules of simple Lie algebras. The quotient algebras of this new constructed Lie algebras are non-solvable complete Lie algebras with l-step nilpotent radicals.展开更多
This paper gives some su?cient conditions for the commutativity of quasi-toral restricted Lie algebras and characterizes some properties on semisimple quasi-toral restricted Lie algebras.
基金Project supported by the the National Natural Science Foundation of China (No. 19971044) the Doctoral Program Foundation of the Ministry of Education of China (No. 97005511).
文摘The authors first give a necessary and sufficient condition for some solvable Lie algebras with l-step nilpotent radicals to be complete, and then construct a new class of infinite dimensional complete Lie algebras by using the modules of simple Lie algebras. The quotient algebras of this new constructed Lie algebras are non-solvable complete Lie algebras with l-step nilpotent radicals.
基金Project supported by the Youth Science Foundation of Northeast Normal University (No.111494027)and the National Natural Science Foundation of China (No.10271076).
文摘This paper gives some su?cient conditions for the commutativity of quasi-toral restricted Lie algebras and characterizes some properties on semisimple quasi-toral restricted Lie algebras.
