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Some generalizations of universal enveloping algebras and bilinear forms on them

N. N. Shapovalov

Mechanical Engineering Institute RAS, Moscow

Abstract: Тhе paper is devoted to description of some results obtained recently by the author in the field of study of universal enveloping algebras of complex reductive Lie algebras and some their extensions. Namely, extensions of enveloping algebras of this kind and of bilinear forms on them and also some related modules and algebras to algebras over rational function fields on Cartan subalgebras are considered.

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

UDC: 512.813.4

Received: 12.02.2010

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