IN this note the infinite-dimensional Lie superalgebras of Cartan type X(m,n)(X=W,S,H or K)over field F of prime characteristic are constructed.Then the second class of finite-dimensional Lie superalgebras of Cartan t...IN this note the infinite-dimensional Lie superalgebras of Cartan type X(m,n)(X=W,S,H or K)over field F of prime characteristic are constructed.Then the second class of finite-dimensional Lie superalgebras of Cartan type over F is defined.Their simplicity and re-strictability are discussed.Finally a conjecture about classification of the展开更多
Let F be a field and char F = p > 3. In this paper the derivation algebras of Lie superalgebras W and S of Cartan-type over F are determined by the calculating method.
Let F be a field of characteristic p>3, and L=_(i≥-1) L_i the finite-dimensional transitive Z-graded simple Lie superalgebra over F. In this paper L is determined if the Z-graded Lie superalgebra L_(-1) L_O is is...Let F be a field of characteristic p>3, and L=_(i≥-1) L_i the finite-dimensional transitive Z-graded simple Lie superalgebra over F. In this paper L is determined if the Z-graded Lie superalgebra L_(-1) L_O is isomorphic to the L_(-1) pl(L_(-1)) or L_(-1)spl(L_(-1)).展开更多
Based on the constructed Lie superalgebra, the super-classical-Boussinesq hierarchy is obtained. Then, its super- Hamiltonian structure is obtained by making use of super=trace identity. Furthermore, the super-classic...Based on the constructed Lie superalgebra, the super-classical-Boussinesq hierarchy is obtained. Then, its super- Hamiltonian structure is obtained by making use of super=trace identity. Furthermore, the super-classical-Boussinesq hierarchy is also integrable in the sense of Liouville.展开更多
This paper presents a sufficient condition for the cohomology groups of an associative superalgebra to vanish. As its application, we prove that the cohomology groups H n(L,M) vanish when L is a strongly semi...This paper presents a sufficient condition for the cohomology groups of an associative superalgebra to vanish. As its application, we prove that the cohomology groups H n(L,M) vanish when L is a strongly semisimple Lie superalgebra and M is an irreducible faithful L module.展开更多
The principal filtration of the infinite-dimensional odd contact Lie superalgebra over a field of characteristic p 〉 2 is proved to be invariant under the automorphism group by investigating ad-nilpotent elements and...The principal filtration of the infinite-dimensional odd contact Lie superalgebra over a field of characteristic p 〉 2 is proved to be invariant under the automorphism group by investigating ad-nilpotent elements and determining certain invariants such as subalgebras generated by some ad-nilpotent elements. Then, it is proved that two automorphisms coincide if and only if they coincide on the -1 component with respect to the principal grading. Finally, all the odd contact superalgebras are classified up to isomorphisms.展开更多
Balinsky–Novikov superalgebras were introduced by Balinsky for constructing super-Virasoro type Lie superalgebras. In this paper, we give sufficient and necessary conditions for a Lie superalgebra generalized by a Ba...Balinsky–Novikov superalgebras were introduced by Balinsky for constructing super-Virasoro type Lie superalgebras. In this paper, we give sufficient and necessary conditions for a Lie superalgebra generalized by a Balinsky–Novikov superalgebra with dimension 2|2 to be a quadratic Lie superalgebra.展开更多
By using the idea of Wakimoto＇s free field, we construct a class of representations for the Lie superalgebra D（2, 1; α） on the tensor product of a polynomial algebra and an exterior algebra involving one parameter...By using the idea of Wakimoto＇s free field, we construct a class of representations for the Lie superalgebra D（2, 1; α） on the tensor product of a polynomial algebra and an exterior algebra involving one parameter A. Then we obtain the necessary and sufficient condition for the representations to be irreducible. In fact. the representation is irreducible if and only if the parameter ,λ satisfies （λ＋m）（λ-1＋α/αm）≠0 for any m∈Z＋.展开更多
文摘IN this note the infinite-dimensional Lie superalgebras of Cartan type X(m,n)(X=W,S,H or K)over field F of prime characteristic are constructed.Then the second class of finite-dimensional Lie superalgebras of Cartan type over F is defined.Their simplicity and re-strictability are discussed.Finally a conjecture about classification of the
文摘Let F be a field and char F = p > 3. In this paper the derivation algebras of Lie superalgebras W and S of Cartan-type over F are determined by the calculating method.
文摘Let F be a field of characteristic p>3, and L=_(i≥-1) L_i the finite-dimensional transitive Z-graded simple Lie superalgebra over F. In this paper L is determined if the Z-graded Lie superalgebra L_(-1) L_O is isomorphic to the L_(-1) pl(L_(-1)) or L_(-1)spl(L_(-1)).
基金supported by the Natural Science Foundation of Shanghai (Grant No. 09ZR1410800)the Science Foundation of the Key Laboratory of Mathematics Mechanization (Grant No. KLMM0806)+1 种基金the Shanghai Leading Academic Discipline Project (Grant No. J50101)the Key Disciplines of Shanghai Municipality (S30104)
文摘Based on the constructed Lie superalgebra, the super-classical-Boussinesq hierarchy is obtained. Then, its super- Hamiltonian structure is obtained by making use of super=trace identity. Furthermore, the super-classical-Boussinesq hierarchy is also integrable in the sense of Liouville.
文摘This paper presents a sufficient condition for the cohomology groups of an associative superalgebra to vanish. As its application, we prove that the cohomology groups H n(L,M) vanish when L is a strongly semisimple Lie superalgebra and M is an irreducible faithful L module.
文摘The principal filtration of the infinite-dimensional odd contact Lie superalgebra over a field of characteristic p 〉 2 is proved to be invariant under the automorphism group by investigating ad-nilpotent elements and determining certain invariants such as subalgebras generated by some ad-nilpotent elements. Then, it is proved that two automorphisms coincide if and only if they coincide on the -1 component with respect to the principal grading. Finally, all the odd contact superalgebras are classified up to isomorphisms.
基金Supported by National Natural Science Foundation of China(Grant No.11401425)
文摘Balinsky–Novikov superalgebras were introduced by Balinsky for constructing super-Virasoro type Lie superalgebras. In this paper, we give sufficient and necessary conditions for a Lie superalgebra generalized by a Balinsky–Novikov superalgebra with dimension 2|2 to be a quadratic Lie superalgebra.
基金Supported by NSF of China(Grant Nos.11701340 and 11271043)
文摘By using the idea of Wakimoto＇s free field, we construct a class of representations for the Lie superalgebra D（2, 1; α） on the tensor product of a polynomial algebra and an exterior algebra involving one parameter A. Then we obtain the necessary and sufficient condition for the representations to be irreducible. In fact. the representation is irreducible if and only if the parameter ,λ satisfies （λ＋m）（λ-1＋α/αm）≠0 for any m∈Z＋.
