Some Generalizations of Universal Enveloping Algebras and Bilinear Forms on them / Shapovalov N.N. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2011. ? 5. P. 44-46 [Moscow Univ. Math. Bulletin. Vol. 66, N 5, 2011.].

The paper is focused on the description of recent results obtained by the author in the field of universal enveloping algebras of complex reductive Lie algebras and some their extensions. Namely, the generalizations of enveloping algebras of this kind and of bilinear forms on them and also some related modules and algebras to the cases of algebras over fields of rational functions on Cartan subalgebras are considered.

Key words: Lie algebra, enveloping algebra, free module, root system, bilinear form, weighted subspace.