This paper is devoted to the structure of complete and perfect Jordan algebras,which are called sympathetic Jordan algebras here.In particular,every perfect Jordan algebra J contains a greatest special sympathetic ide...This paper is devoted to the structure of complete and perfect Jordan algebras,which are called sympathetic Jordan algebras here.In particular,every perfect Jordan algebra J contains a greatest special sympathetic ideal M and a decomposition into direct sum of ideals about the greatest special sympathetic ideal.Besides,each perfect Jordan algebra J also contains a solvable ideal P(J)which is greatest among the solvable ideals K of J such that K∩M={0}and a decomposition into direct sum of subalgebras J=m+P(J),where m is a sympathetic subalgebra of J,which is similar to the Levi decomposition of Lie algebras.Moreover,J is sympathetic if and only if P(J)={0}.What is more,a class of ideals of Jordan algebras such that the quotients are sympathetic Jordan algebras are studied and some vital properties about this kind of ideal are highlighted.展开更多
基金Supported by NNSF of China(Nos.12271085,12071405)NSF of Jilin Province(No.YDZJ202201ZYTS589)the Fundamental Research Funds for the Central Universities and Heilongjiang Provincial Universities Basic Scientific Research Operation Fund Project of Heilongjiang University(No.2022-KYYWF-1114).
文摘This paper is devoted to the structure of complete and perfect Jordan algebras,which are called sympathetic Jordan algebras here.In particular,every perfect Jordan algebra J contains a greatest special sympathetic ideal M and a decomposition into direct sum of ideals about the greatest special sympathetic ideal.Besides,each perfect Jordan algebra J also contains a solvable ideal P(J)which is greatest among the solvable ideals K of J such that K∩M={0}and a decomposition into direct sum of subalgebras J=m+P(J),where m is a sympathetic subalgebra of J,which is similar to the Levi decomposition of Lie algebras.Moreover,J is sympathetic if and only if P(J)={0}.What is more,a class of ideals of Jordan algebras such that the quotients are sympathetic Jordan algebras are studied and some vital properties about this kind of ideal are highlighted.
