There have been a great many of studies on the pointed representations of fi- nite-dimensional sanple Lie algebras.cf.[1][2]etc.In this paper we give a new proof of an impottant Lemma,and from this we derive our main ...There have been a great many of studies on the pointed representations of fi- nite-dimensional sanple Lie algebras.cf.[1][2]etc.In this paper we give a new proof of an impottant Lemma,and from this we derive our main result:Irreducible pointed modules of finite -dimesional simple Lie algebras are all Harish-Chandra modules.展开更多
In this paper, we prove the generalized Hyers-Ulam stability of homomorphisms in quasi- Banach algebras associated with the following Pexiderized Jensen functional equation f（x＋y/2＋z）-g（x-y/2＋z）=h（y）.This is...In this paper, we prove the generalized Hyers-Ulam stability of homomorphisms in quasi- Banach algebras associated with the following Pexiderized Jensen functional equation f（x＋y/2＋z）-g（x-y/2＋z）=h（y）.This is applied to investigating homomorphisms between quasi-Banach algebras. The concept of the generalized Hyers-Ulam stability originated from Rassias＇ stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72, 297-300 （1978）.展开更多
Our motivation is to build a systematic method in order to investigate the structure of cluster algebras of geometric type. The method is given through the notion of mixing-type sub-seeds, the theory of seed homomorph...Our motivation is to build a systematic method in order to investigate the structure of cluster algebras of geometric type. The method is given through the notion of mixing-type sub-seeds, the theory of seed homomorphisms and the view-point of gluing of seeds. As an application, for(rooted) cluster algebras, we completely classify rooted cluster subalgebras and characterize rooted cluster quotient algebras in detail. Also,we build the relationship between the categorification of a rooted cluster algebra and that of its rooted cluster subalgebras. Note that cluster algebras of geometric type studied here are of the sign-skew-symmetric case.展开更多
文摘There have been a great many of studies on the pointed representations of fi- nite-dimensional sanple Lie algebras.cf.[1][2]etc.In this paper we give a new proof of an impottant Lemma,and from this we derive our main result:Irreducible pointed modules of finite -dimesional simple Lie algebras are all Harish-Chandra modules.
文摘In this paper, we prove the generalized Hyers-Ulam stability of homomorphisms in quasi- Banach algebras associated with the following Pexiderized Jensen functional equation f（x＋y/2＋z）-g（x-y/2＋z）=h（y）.This is applied to investigating homomorphisms between quasi-Banach algebras. The concept of the generalized Hyers-Ulam stability originated from Rassias＇ stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72, 297-300 （1978）.
基金supported by National Natural Science Foundation of China (Grant Nos. 11671350 and 11571173)
文摘Our motivation is to build a systematic method in order to investigate the structure of cluster algebras of geometric type. The method is given through the notion of mixing-type sub-seeds, the theory of seed homomorphisms and the view-point of gluing of seeds. As an application, for(rooted) cluster algebras, we completely classify rooted cluster subalgebras and characterize rooted cluster quotient algebras in detail. Also,we build the relationship between the categorification of a rooted cluster algebra and that of its rooted cluster subalgebras. Note that cluster algebras of geometric type studied here are of the sign-skew-symmetric case.
