FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 2, PAGES 607-616

A necessary condition of co-length finiteness of Lie algebra variety in the case of zero-characteristic field

I. R. Khanina

Abstract

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This article examines how some characteristics of Lie algebra variety like co-length are connected with the variety structure in the case of zero-characteristic field. In particular, it is proved that co-length finiteness for the variety $V$ implies the inclusion $U$₂ Ë V Ì N_s A, where $s$ is some natural number, and, as a consequence, the polynomial growth of the variety $V$.

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Last modified: September 1, 2000