An explicit construction of irreducible representations for the affine-Virasoro Lie algebra of type Bl, through the use of vertex operators and certain oscillator representations of the Virasoro algebra, is given.
In this paper F always denotes a field of characteristic p 〉 2. We construct the finitedimensional modular Lie superalgebra W（m,n, l, t_） over a field F, define θ-type derivation and determine the derivation superalgebra of W（m, n, l, t_）.
In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer（L）and central extension H^2（L,F）on some Lie color algebras.Meanwhile,they generalize the notion of double extension to quadratic Lie color algebras,a sufficient condition for a quadratic Lie color algebra to be a double extension and further properties are given.
In this article the ■-graded transitive modular Lie superalgebra ⊕_(i≥-1)L_i,whose repre- sentation of L_o in L_(-1)is isomorphic to the natural representation of osp(L_(-1)),is determined.
The natural filtrations of the general algebra \(\overline W \) and the special algebra \(\overline S \) of formal vectorfields are proved to be invariant. Furthermore, the automorphism groups of \(\overline W \) and \(\overline S \) are proved to be isomorphic to the corresponding admissible automorphism groups of the base superalgebra U. Then the automorphisms of \(\overline W \) or \(\overline S \) can be induced by the continue automorphisms of U.
