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 A 1 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 ?v (v ≥ 1), and then construct an extended affine Lie algebra of type A 1 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 ?2 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 ?2-graded automorphisms of the TKK algebra T(J(S)).
