Suppose that F is a field of characteristic zero and (ⅰ) D is a finite-dimensional central division algabra over F; (ⅱ) A is a finite-dimensional semi-simple algabra over F. It is proved that as F-algebras, D and A ...Suppose that F is a field of characteristic zero and (ⅰ) D is a finite-dimensional central division algabra over F; (ⅱ) A is a finite-dimensional semi-simple algabra over F. It is proved that as F-algebras, D and A can be generated by two elements respectively.展开更多
By using Artin-Wedderburn Theorem and the decomp- osition of central edepotent, several results about normality on closed subsets in standard table algebras are generalized to complex semi-simple algebras and the proo...By using Artin-Wedderburn Theorem and the decomp- osition of central edepotent, several results about normality on closed subsets in standard table algebras are generalized to complex semi-simple algebras and the proofs are easier than the original ones.展开更多
By making use of the classification of real simple Lie algebra, we get the maximum of the squared length of restricted roots case by case, and thus get the upper bounds of sectional curvature for irreducible Riemannia...By making use of the classification of real simple Lie algebra, we get the maximum of the squared length of restricted roots case by case, and thus get the upper bounds of sectional curvature for irreducible Riemannian symmetric spaces of compact type. As an application, this paper verifies Sampson＇s conjecture in most cases for irreducible Riemannian symmetric spaces of noncompact type.展开更多
In this paper, the partial positivity （resp., negativity） of the curvature of all irreducible Riemannian symmetric spaces is determined. From the classifications of abstract root systems and maximal subsystems, the ...In this paper, the partial positivity （resp., negativity） of the curvature of all irreducible Riemannian symmetric spaces is determined. From the classifications of abstract root systems and maximal subsystems, the author gives the calculations for symmetric spaces both in classical types and in exceptional types.展开更多
In this paper, we mainly investigate the realization of 3-Lie algebras from a family of Lie algebras. We prove the realization theorem, offer a concrete example realizing all type of 4-dimensional 3-Lie algebras, and ...In this paper, we mainly investigate the realization of 3-Lie algebras from a family of Lie algebras. We prove the realization theorem, offer a concrete example realizing all type of 4-dimensional 3-Lie algebras, and also give some properties about semi-simple n-Lie algebras.展开更多
文摘Suppose that F is a field of characteristic zero and (ⅰ) D is a finite-dimensional central division algabra over F; (ⅱ) A is a finite-dimensional semi-simple algabra over F. It is proved that as F-algebras, D and A can be generated by two elements respectively.
基金Supported by the National Natural Science Foundation of China(11571129)Educational Commission of Hubei Province(D20132804)
文摘By using Artin-Wedderburn Theorem and the decomp- osition of central edepotent, several results about normality on closed subsets in standard table algebras are generalized to complex semi-simple algebras and the proofs are easier than the original ones.
文摘By making use of the classification of real simple Lie algebra, we get the maximum of the squared length of restricted roots case by case, and thus get the upper bounds of sectional curvature for irreducible Riemannian symmetric spaces of compact type. As an application, this paper verifies Sampson＇s conjecture in most cases for irreducible Riemannian symmetric spaces of noncompact type.
文摘In this paper, the partial positivity （resp., negativity） of the curvature of all irreducible Riemannian symmetric spaces is determined. From the classifications of abstract root systems and maximal subsystems, the author gives the calculations for symmetric spaces both in classical types and in exceptional types.
文摘In this paper, we mainly investigate the realization of 3-Lie algebras from a family of Lie algebras. We prove the realization theorem, offer a concrete example realizing all type of 4-dimensional 3-Lie algebras, and also give some properties about semi-simple n-Lie algebras.
