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 dete...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
In this paper we study the homology and cohomology groups of the super Schrodinger algebra S(1/1)in(1+l)-dimensional spacetime.We explicitly compute the homology groups of S(1/1)with coefficients in the trivial module...In this paper we study the homology and cohomology groups of the super Schrodinger algebra S(1/1)in(1+l)-dimensional spacetime.We explicitly compute the homology groups of S(1/1)with coefficients in the trivial module.Then using duality,we finally obtain the dimensions of the cohomology groups of S(1/1)with coefficients in the trivial module.展开更多
We explicitly compute the first and second cohomology groups of the SchrSdinger algebra S（1） with coefficients in the trivial module and the finite-dimensional irreducible modules. We also show that the first and se...We explicitly compute the first and second cohomology groups of the SchrSdinger algebra S（1） with coefficients in the trivial module and the finite-dimensional irreducible modules. We also show that the first and second cohomology groups of S（1） with coefficients in the universal enveloping algebras U（S（1）） （under the adjoint action） are infinite dimensional.展开更多
We study the N=1 super Schrdinger algebra S in(1+1)-dimensional spacetime. The first part of this paper determines the necessary and sufficient conditions for highest weight supermodules over S to be simple. The paper...We study the N=1 super Schrdinger algebra S in(1+1)-dimensional spacetime. The first part of this paper determines the necessary and sufficient conditions for highest weight supermodules over S to be simple. The paper also describes the structure of all Verma supermodules and determines all simple Harish-Chandra supermodules over S.展开更多
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In this paper we study the homology and cohomology groups of the super Schrodinger algebra S(1/1)in(1+l)-dimensional spacetime.We explicitly compute the homology groups of S(1/1)with coefficients in the trivial module.Then using duality,we finally obtain the dimensions of the cohomology groups of S(1/1)with coefficients in the trivial module.
基金Supported by National Natural Science Foundation of China(Grant No.11271056)Jiangsu Overseas Research & Training Program for University Prominent Young & Middle-aged Teachers and Presidentsthe Fundamental Research Funds for the Central Universities
文摘We explicitly compute the first and second cohomology groups of the SchrSdinger algebra S（1） with coefficients in the trivial module and the finite-dimensional irreducible modules. We also show that the first and second cohomology groups of S（1） with coefficients in the universal enveloping algebras U（S（1）） （under the adjoint action） are infinite dimensional.
基金supported by the China Scholar Council for the financial
文摘We study the N=1 super Schrdinger algebra S in(1+1)-dimensional spacetime. The first part of this paper determines the necessary and sufficient conditions for highest weight supermodules over S to be simple. The paper also describes the structure of all Verma supermodules and determines all simple Harish-Chandra supermodules over S.
