Max-factor paradigm and finite-dimensional representations of Lie algebras / Yu. P. Razmyslov, G. A. Pogudin. //Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2012. ? 4. P. 48-50 [Moscow Univ. Math. Bulletin. Vol. 67, N 4, 2012.].

An isomorphism between formal power series algebra and dual space to universal enveloping algebra is presented. The image of maximal locally finite dimensional submodule under it lies in preimage of rational functions algebra under Borel transform.

Key words: derivation, divided power series algebra, universal enveloping algebra, maximal locally finite dimensional submodule, Lie algebra, Borel transform.