FPM 2004, vol. 10, no. 4, pp. 97-106

FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2004, VOLUME 10, NUMBER 4, PAGES 97-106

Free Malcev superalgebra on one odd generator and related superalgebras

N. M. Zhukavets
I. P. Shestakov

Abstract

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A base of the universal multiplicative envelope of the free Malcev superalgebra $$ \mathcal
M $$ on one odd generator is constructed. Some corollaries for skew-symmetric functions and central elements in free Malcev and free alternative algebras are obtained. Moreover, a base of the Poisson--Malcev superalgebra of $$ \mathcal M
$$ is constructed. As a corollary, a set of elements that spans the free alternative superalgebra on one odd generator is obtained.

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