Derivations of the Even Part of the Odd Hamiltonian Superalgebra in Modular Case

In this paper we mainly study the derivations for even part of the finite-dimensional odd Hamiltonian superalgebra HO over a field of prime characteristic. We first give the generating set of the even part g of HO. Then we compute the derivations from g into the even part m of the generalized Witt superalgebra. Finally, we determine the derivation algebra and outer derivation algebra of and the dimension formulas. In particular, the first cohomology groups H^1（g;m） and H^1（g;g） are determined.

Lie Bialgebras of Generalized Virasoro-like Type

In this paper, Lie bialgebra structures on generalized Virasoro-like algebras are studied. It is proved that all such Lie bialgebras are triangular coboundary.

Classification of Irreducible Weight Modules with a Finite-dimensional Weight Space over Twisted Heisenberg-Virasoro Algebra

We show that the support of an irreducible weight module over the twisted Heisenberg-Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite dimensional. As a corollary, we obtain that every irreducible weight module over the twisted Heisenber-Virasoro algebra, having a nontrivial finite-dimensional weight space, is a Harish-Chandra module （and hence is either an irreducible highest or lowest weight module or an irreducible module from the intermediate series）.

Irreducible Weight Modules over the Twisted SchrSdinger-Virasoro Algebra

It is shown that the support of an irreducible weight module over the SchrSdinger-Virasoro Lie algebra with an infinite-dimensional weight space coincides with the weight lattice, and all nontrivial weight spaces of such a module are infinite-dimensional. As a by-product, it is obtained that every simple weight module over Lie algebra of this type with a nontrivial finite-dimensional weight space is a Harish-Chandra module.

Highest Weight Representations of a Family of Lie Algebras of Block Type

For an additive subgroup G of a field F of characteristic zero, a Lie algebra B（G） of Block type is defined with basis {Lα,i｜ α∈G, i∈Z＋} and relations [Lα,i, Lβ,j] = （β-α）Lα＋β,i＋j＋（αj-βi）Lα＋β,Lα＋β,i＋j-1.It is proved that an irreducible highest weight B（Z）-module is quasifinite if and only if it is a proper quotient of a Verma module. Furthermore, for a total order λ on G and any ∧∈B（G）0^＊（the dual space of B（G）0 = span{L0,i｜i∈Z＋}）, a Verma B（G）-module M（∧,λ） is defined, and the irreducibility of M（A,λ） is completely determined.

Dual Lie Bialgebra Structures of W-algebra W(2, 2) Type

In the present paper, we investigate the dual Lie coalgebras of the centerless W(2,2) algebra by studying the maximal good subspaces. Based on this, we construct the dual Lie bialgebra structures of the centerless W(2,2) Lie bialgebra. As by-products, four new infinite dimensional Lie algebras are obtained.