Let L be the derivation Lie algebra of C[t1^±1 , t2^±1 ]. Given a triangle decomposition L = L＋ η ＋ L-, we define a nonsingular Lie algebra homomorphism φ ： L＋ → C and the universal Whittaker L-module...Let L be the derivation Lie algebra of C[t1^±1 , t2^±1 ]. Given a triangle decomposition L = L＋ η ＋ L-, we define a nonsingular Lie algebra homomorphism φ ： L＋ → C and the universal Whittaker L-module We of type φ. We obtain all Whittaker vectors and submodules of We. Moreover, all simple Whittaker L-modules of type φ are determined.展开更多
Letβbe a complex number,and a class of non-semisimple and non-solvable rank two Lie conformal algebras L(β)are introduced.In this paper,conformal derivations,conformal quasiderivations,generalized conformal derivati...Letβbe a complex number,and a class of non-semisimple and non-solvable rank two Lie conformal algebras L(β)are introduced.In this paper,conformal derivations,conformal quasiderivations,generalized conformal derivations and conformal biderivations of L(β)are studied.Besides,central extensions and conformal modules of rank one of L(β)are determined.展开更多
We construct two kinds of infinite-dimensional 3-Lie algebras from a given commutative associative algebra, and show that they are all canonical Nambu 3-Lie algebras. We relate their inner derivation algebras to Witt ...We construct two kinds of infinite-dimensional 3-Lie algebras from a given commutative associative algebra, and show that they are all canonical Nambu 3-Lie algebras. We relate their inner derivation algebras to Witt algebras, and then study the regular representations of these 3-Lie algebras and the natural representations of the inner derivation algebras. In particular, for the second kind of 3-Lie algebras, we find that their regular representations are Harish-Chandra modules, and the inner derivation algebras give rise to intermediate series modules of the Witt algebras and contain the smallest full toroidal Lie algebras without center.展开更多
In this article, we introduce the notion of generalized derivations on Hilbert C＊-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen...In this article, we introduce the notion of generalized derivations on Hilbert C＊-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen type functional equationrf（x＋y/r）＋sg（x-y/s）=2h（x）for r, s ∈ R ／ {0} on Hilbert C＊-modules, where f, g, and h are mappings from a Hilbert C＊-module M to M.展开更多
In this paper, two kinds of skew derivations of a type of Nichols algebras are intro- duced, and then the relationship between them is investigated. In particular they satisfy the quantum Serre relations. Therefore, t...In this paper, two kinds of skew derivations of a type of Nichols algebras are intro- duced, and then the relationship between them is investigated. In particular they satisfy the quantum Serre relations. Therefore, the algebra generated by these derivations and corresponding automorphisms is a homomorphic image of the Drinfeld-Jimbo quantum enveloping algebra Uq^＋（g）, which proves the Nichols algebra becomes a/gq（g）-module algebra. But the Nichols algebra considered here is exactly Uq^＋（g）, namely, the positive part of the Drinfeld-Jimbo quantum enveloping algebra Uq^＋（g）, it turns out that Uq^＋（g） is aUq^＋（g）-module algebra.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.11571145 and 11271165)the Youth Foundation of National Natural Science Foundation of China(Grant Nos.11101350 and 11302052)the Natural Science Foundation of Fujian Province(Grant No.2010J05001)
文摘Let L be the derivation Lie algebra of C[t1^±1 , t2^±1 ]. Given a triangle decomposition L = L＋ η ＋ L-, we define a nonsingular Lie algebra homomorphism φ ： L＋ → C and the universal Whittaker L-module We of type φ. We obtain all Whittaker vectors and submodules of We. Moreover, all simple Whittaker L-modules of type φ are determined.
基金supported by the National Natural Science Foundation of China(Grant No.11171183)the Shandong Provincial Natural Science Foundation of China(Grant No.ZR2011AM013)
基金Supported by the National Natural Science Foundation of China(11661063,11971350)a grant from China Scholarship Council(201708645021)the Fundamental Research Funds for the Central Universities(2019QNA34).
文摘Letβbe a complex number,and a class of non-semisimple and non-solvable rank two Lie conformal algebras L(β)are introduced.In this paper,conformal derivations,conformal quasiderivations,generalized conformal derivations and conformal biderivations of L(β)are studied.Besides,central extensions and conformal modules of rank one of L(β)are determined.
基金This work was supported in part by the National Natural Science Foundation of China （Grant No. 11371245） and the Natural Science Foundation of Hebei Province, China （Grant No. A2014201006）.
文摘We construct two kinds of infinite-dimensional 3-Lie algebras from a given commutative associative algebra, and show that they are all canonical Nambu 3-Lie algebras. We relate their inner derivation algebras to Witt algebras, and then study the regular representations of these 3-Lie algebras and the natural representations of the inner derivation algebras. In particular, for the second kind of 3-Lie algebras, we find that their regular representations are Harish-Chandra modules, and the inner derivation algebras give rise to intermediate series modules of the Witt algebras and contain the smallest full toroidal Lie algebras without center.
文摘In this article, we introduce the notion of generalized derivations on Hilbert C＊-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen type functional equationrf（x＋y/r）＋sg（x-y/s）=2h（x）for r, s ∈ R ／ {0} on Hilbert C＊-modules, where f, g, and h are mappings from a Hilbert C＊-module M to M.
基金Supported by the National Natural Science Foundation of China (Grant No.10771182)
文摘In this paper, two kinds of skew derivations of a type of Nichols algebras are intro- duced, and then the relationship between them is investigated. In particular they satisfy the quantum Serre relations. Therefore, the algebra generated by these derivations and corresponding automorphisms is a homomorphic image of the Drinfeld-Jimbo quantum enveloping algebra Uq^＋（g）, which proves the Nichols algebra becomes a/gq（g）-module algebra. But the Nichols algebra considered here is exactly Uq^＋（g）, namely, the positive part of the Drinfeld-Jimbo quantum enveloping algebra Uq^＋（g）, it turns out that Uq^＋（g） is aUq^＋（g）-module algebra.
