Let DerA be the Lie algebra of derivations of the d-torus A = C[t1± 1, . . . , td±1]. By applying Shen-Larsson’s functors we get a class of indecomposable DerA-modules from finite-dimensional indecomposable gld-modules. We also give a complete description of the submodules of these indecomposable DerA-modules. Our results generalize those obtained by Rao.
The classification of extended affine Lie algebras of type A1 depends on the Tits-Kantor- Koecher （TKK） algebras constructed from semilattices of Euclidean spaces.One can define a unitary Jordan algebra J（S） from a semilattice S of Rv （v≥1）,and then construct an extended affine Lie algebra of type A1 from the TKK algebra T（J（S）） which is obtained from the Jordan algebra J（S） by the so-called Tits-Kantor-Koecher construction.In R2 there are only two non-similar semilattices S and S′,where S is a lattice and S′is a non-lattice semilattice.In this paper we study the Z2-graded automorphisms of the TKK algebra T（J（S））.
