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
It is observed that a classical group over a finite ring R with identity can be reduced to that over finite fields after the procedures of taking “modulo the radical”, “direct sum” and “tensor products”. B...It is observed that a classical group over a finite ring R with identity can be reduced to that over finite fields after the procedures of taking “modulo the radical”, “direct sum” and “tensor products”. Basing on that fact, we calculate the orders of classical groups over R and the number of k dimensional free submodules of an n dimensional free module over R .展开更多
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.
文摘It is observed that a classical group over a finite ring R with identity can be reduced to that over finite fields after the procedures of taking “modulo the radical”, “direct sum” and “tensor products”. Basing on that fact, we calculate the orders of classical groups over R and the number of k dimensional free submodules of an n dimensional free module over R .
