FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1997, VOLUME 3, NUMBER 2, PAGES 435-451

V. M. Zhuravlev

Abstract

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In the article we consider verbal ideals of the free
finite-generated
Lie algebras over field of zero characteristic.
This ideals are connected with an action
of the universal envelopment algebra
of the Lie algebra of derivations of
a free finite-generated Lie algebra.
We estimate the multiplicities of the irreducible components in the
modules of the concequences of the identities.
For the homogeneous identities
which generate the irreducible module of degree
```$n$ ,
we study the decomposition
to irreducible components his module of consequences degree of $n+1$ .

In the case two-generated of the free Lie algebra we also find the
vectors oldest weight in these irreducible components.

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