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The baby Tits-Kantor-Koecher (TKK) algebra constructed from the smallest (nonlattice) semilattice is related to the “smallest” extended affine Lie algebras other than the finite dimensional simple Lie algebras and the affine Kac-Moody algebras. In this article, we classify the finite dimensional irreducible representations for the baby TKK algebra. It turns out that such representations can be lifted from modules of direct sums of finitely many copies of the simple Lie algebra sp4(). [ABSTRACT FROM AUTHOR]

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]

Abstract: Let be the universal central extension of a graded Lie algebra of Block type. In this paper, it is proved that any quasifinite irreducible -module is either highest weight, lowest weight or uniformly bounded. Furthermore, the quasifinite irreducible highest weight -modules are classified, and the intermediate series -modules are classified and constructed. [Copyright &y& Elsevier]

Abstract: Let be the q-analog Virasoro-like algebra. In this paper we prove that any Harish-Chandra module of with nontrivial center is isomorphic to a generalized highest weight module. Moreover, we show that a generalized highest weight Harish-Chandra module of is induced from an irreducible module of a Heisenberg subalgebra of . [Copyright &y& Elsevier]

Abstract: In the present paper, we study the nonzero level Harish-Chandra modules for the Virasoro-like algebra. We prove that a nonzero level Harish-Chandra module of the Virasoro-like algebra is a generalized highest weight (GHW for short) module. Then we prove that a GHW module of the Virasoro-like algebra is induced from an irreducible module of a Heisenberg subalgebra. [Copyright &y& Elsevier]