DISTRIBUTIONS OVER AN ALGEBRA OF TRUNCATED POLYNOMIALS

Abstract

We study integrable distributions over the -algebra of truncated polynomials, where is a field of characteristic . We obtain an analogue of the theorem of Frobenius; we describe the equivalence classes of TI-distributions, i.e., of those distributions with respect to which the algebra has no nontrivial -invariant ideals; we show that over a perfect field any TI-distribution is equivalent to a general Lie algebra of Cartan type ; and we find all the forms of the Zassenhaus algebra, in the process making essential use of the theory of representations of the chromatic quiver of Kronecker.Bibliography: 13 titles.