FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1997, VOLUME 3, NUMBER 2, PAGES 625-630

Recognition of identities in quotient algebras of universal enveloping algebras

E. V. Loukoianova (Loukoyanova)

Abstract

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For special type of (associative) polynomials f and simple algebras L the problem of recognition of identity f in quotient algebra UL/J of universal enveloping algebra UL by arbitrary ideal J, where J is given by its generators, is solved. The central point of the solution is the

Theorem. Let l1, ¼ ,lp be Lie (associative) polynomials with non-intersecting sets of variables which are not identities in L, f = Pi=1p li(xi1,¼, xini), then the verbal ideal Tf(UL) generated by polynomial f in UL is equal to ULp.

In particular, UL/Tf(UL) is a nilpotent algebra of degree p.


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