Over a fieldF of arbitrary characteristic, we define the associative and the Lie algebras of Weyl type on the same vector spaceA[D] =A?F[D] from any pair of a commutative associative algebra,A with an identity element...Over a fieldF of arbitrary characteristic, we define the associative and the Lie algebras of Weyl type on the same vector spaceA[D] =A?F[D] from any pair of a commutative associative algebra,A with an identity element and the polynomial algebraF[D] of a commutative derivation subalgebraD ofA We prove thatA[D], as a Lie algebra (modulo its center) or as an associative algebra, is simple if and only ifA isD-simple andA[D] acts faithfully onA. Thus we obtain a lot of simple algebras.展开更多
Over an algebraically closed field of characteristic p>2,based on the results on the representation theory of special linear Lie algebra sl(2),restricted simple modules L(λ)of the Schrodinger algebra S(1)are deter...Over an algebraically closed field of characteristic p>2,based on the results on the representation theory of special linear Lie algebra sl(2),restricted simple modules L(λ)of the Schrodinger algebra S(1)are determined,and all derivations of S(1)on L(λ)are also obtained.As an application,the first cohomology of S(1)with the coefficient in L(λ)is determined.展开更多
The author constructs a class of indecomposable non-degenerate solvable Lie Algebras corresponding to a Cartan matrix A over the field of complex numbers and we determine all their derivations.
In one of our recent papers, the associative and the Lie algebras of Weyl type A[D] = A F[D] were defined and studied, where A is a commutative associative algebra with an identity element over a field F of any charac...In one of our recent papers, the associative and the Lie algebras of Weyl type A[D] = A F[D] were defined and studied, where A is a commutative associative algebra with an identity element over a field F of any characteristic, and F[D] is the polynomial algebra of a commutative derivation subalgebra D of A. In the present paper, a class of the above associative and Lie algebras A[D] with F being a field of characteristic 0, D consisting of locally finite but not locally nilpotent derivations of A, are studied. The isomorphism classes and automorphism groups of these associative and Lie algebras are determined.展开更多
The main result of this paper is that every derivation of the finite-dimensional simple modular Lie superalgebra S（n） is inner, and S（n） has no nonsingular associative form.
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
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19801037) a Fund from National Education Ministry of China.
文摘Over a fieldF of arbitrary characteristic, we define the associative and the Lie algebras of Weyl type on the same vector spaceA[D] =A?F[D] from any pair of a commutative associative algebra,A with an identity element and the polynomial algebraF[D] of a commutative derivation subalgebraD ofA We prove thatA[D], as a Lie algebra (modulo its center) or as an associative algebra, is simple if and only ifA isD-simple andA[D] acts faithfully onA. Thus we obtain a lot of simple algebras.
文摘Over an algebraically closed field of characteristic p>2,based on the results on the representation theory of special linear Lie algebra sl(2),restricted simple modules L(λ)of the Schrodinger algebra S(1)are determined,and all derivations of S(1)on L(λ)are also obtained.As an application,the first cohomology of S(1)with the coefficient in L(λ)is determined.
文摘The author constructs a class of indecomposable non-degenerate solvable Lie Algebras corresponding to a Cartan matrix A over the field of complex numbers and we determine all their derivations.
基金This work was supported by the National Natural Science Foundation of China,Hundred Talents Program of Chinese Academy of Sciences and a Fund from National Education Ministry of China. Su Yucai was partially supported by Academy of Mathematics and Syst
文摘In one of our recent papers, the associative and the Lie algebras of Weyl type A[D] = A F[D] were defined and studied, where A is a commutative associative algebra with an identity element over a field F of any characteristic, and F[D] is the polynomial algebra of a commutative derivation subalgebra D of A. In the present paper, a class of the above associative and Lie algebras A[D] with F being a field of characteristic 0, D consisting of locally finite but not locally nilpotent derivations of A, are studied. The isomorphism classes and automorphism groups of these associative and Lie algebras are determined.
基金Supported by the Tianyuan Fund for Mathematics （No. 11126051）, the Heilongjiang Provincial Natural Science Foundation of China （No. A201008）, the Scientific Research Fund of Heilongjiang Provincial Education Department （No. 12511157）, and the Doctoral Fund of Harbin Normal University （No. KJB201105）. This paper was completed when the second author visited the College of William and Mary, and he thanks the university and Professor Junping Shi for warm hospitality.
文摘The main result of this paper is that every derivation of the finite-dimensional simple modular Lie superalgebra S（n） is inner, and S（n） has no nonsingular associative form.
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.
