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
We consider the simple restricted modules for special contact Lie superalgebras of odd type over an algebraically closed field of characteristic p>3.We give a sufficient and necessary condition in terms of typical ...We consider the simple restricted modules for special contact Lie superalgebras of odd type over an algebraically closed field of characteristic p>3.We give a sufficient and necessary condition in terms of typical or atypical weights for restricted Kac modules to be simple.In the process,we also determine the socle for each restricted Kac module and the length for each simple restricted module.展开更多
In this article, we introduce the notions of restricted Lie 2-algebras and crossed modules of restricted Lie algebras, and give a series of examples of restricted Lie 2-algebras. We also construct restricted Lie 2-alg...In this article, we introduce the notions of restricted Lie 2-algebras and crossed modules of restricted Lie algebras, and give a series of examples of restricted Lie 2-algebras. We also construct restricted Lie 2-algebras from A（m）-algebras, restricted Leibniz algebras, restricted right-symmetric algebras. Finally, we prove that there is a one-to-one correspondence between strict restricted Lie 2-algebras and crossed modules of restricted Lie algebras.展开更多
We classify the irreducible restricted modules for the affine Nappi-Witten Lie algebra H4 with some natural conditions. It turns out that the representation theory of H4 is quite different from the theory of represent...We classify the irreducible restricted modules for the affine Nappi-Witten Lie algebra H4 with some natural conditions. It turns out that the representation theory of H4 is quite different from the theory of representations of Heisenberg algebras. We also study the extension of the vertex operator algebra VH4 （e, 0） by the even lattice L. We give the structure of the extension VH4 （e, 0） [L] and its irreducible modules via irreducible representations of VH4（e, 0） viewed as a vertex algebra.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.
基金supported in part by the National Natural Science Foundation of China(Grant No.11701158).
文摘We consider the simple restricted modules for special contact Lie superalgebras of odd type over an algebraically closed field of characteristic p>3.We give a sufficient and necessary condition in terms of typical or atypical weights for restricted Kac modules to be simple.In the process,we also determine the socle for each restricted Kac module and the length for each simple restricted module.
基金Supported by ZJNSF(Grant Nos.LY17A010015 and LZ14A010001)NNSF(Grant No.11171296)
文摘In this article, we introduce the notions of restricted Lie 2-algebras and crossed modules of restricted Lie algebras, and give a series of examples of restricted Lie 2-algebras. We also construct restricted Lie 2-algebras from A（m）-algebras, restricted Leibniz algebras, restricted right-symmetric algebras. Finally, we prove that there is a one-to-one correspondence between strict restricted Lie 2-algebras and crossed modules of restricted Lie algebras.
文摘We classify the irreducible restricted modules for the affine Nappi-Witten Lie algebra H4 with some natural conditions. It turns out that the representation theory of H4 is quite different from the theory of representations of Heisenberg algebras. We also study the extension of the vertex operator algebra VH4 （e, 0） by the even lattice L. We give the structure of the extension VH4 （e, 0） [L] and its irreducible modules via irreducible representations of VH4（e, 0） viewed as a vertex algebra.
