Span of a DL-algebra

Abstract

Unless otherswise specified, all objects are defined over a field k of characteristic 0. Let K be a field. The unessentialness of an extension of the algebra Der K by means of a splittable semisimple Lie algebra is established. Let D_K be the category of differential Lie algebras (DL-algebras) (g;K). In this paper for an extension L/K the functor η:D_K → D_L, defining the tensor product L ⊗ _K of vector spaces and the homomorphism of Lie algebras, is constructed. If the extension L/K is algebraic, then η is unique. The results will be required for strengthening the progress on Gelfand–Kirillov problem and weakened conjecture [1, 2].