First Cohomology Group from the Virasoro-Like Algebra to its Larsson Functor Module.

Let W be the Virasoro-like algebra, and d1, d2 be the degree derivations of W. Set L = W⊕C d1⊕C d2. Let Fα(V) be the L-module defined by Larsson's functor applied to a finite dimensional sl2-module V. In this article, the derivations from L to L-modules Fα(V) and the first cohomology group H1(L, Fα(V)) are given. [ABSTRACT FROM AUTHOR]