  A class of Z_2-graded Lie algebra and Lie superalgebra extensions of the
pseudo-orthogonal algebra of a spacetime of arbitrary dimension and signature
is investigated. They have the form g = g_0 + g_1, with g_0 = so(V) + W_0 and
g_1 = W_1, where the algebra of generalized translations W = W_0 + W_1 is the
maximal solvable ideal of g, W_0 is generated by W_1 and commutes with W.
Choosing W_1 to be a spinorial so(V)-module (a sum of an arbitrary number of
spinors and semispinors), we prove that W_0 consists of polyvectors, i.e. all
the irreducible so(V)-submodules of W_0 are submodules of \Lambda V. We provide
a classification of such Lie (super)algebras for all dimensions and signatures.
The problem reduces to the classification of so(V)-invariant \Lambda^k V-valued
bilinear forms on the spinor module S.
