Supports of weight modules over Witt algebras

As the first step towards a classification of simple weight modules with finite dimensional weight spaces over Witt algebras W-n, we explicitly describe the supports of such modules. We also obtain some descriptions of the support of an arbitrary simple weight module over a Z(n)-graded Lie algebra g having a root space decomposition circle plus(n)(a is an element of Z) g(alpha) with respect to the abelian subalgebra go, with the property [g(alpha), g(beta)] = g(alpha+beta) for all alpha,beta is an element of Z(n), a not equal beta (this class contains the algebra W-n).