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Communications in Algebra Volume 34, 2006 - Issue 4
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Original Articles

The Universal Multiplicative Envelope of the Free Malcev Superalgebra on One Odd Generator

Ivan Shestakov Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, Brasil; Sobolev Institute of Mathematics, Novosibirsk, RussiaCorrespondence[email protected]
&
Natalia Zhukavets Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, Brasil; Faculty of Electrical Engineering, Czech Technical University in Prague, Prague, Czech Republic
Pages 1319-1344 | Received 18 Oct 2004, Published online: 03 Sep 2006
 
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ABSTRACT

A base of the universal multiplicative envelope for the free Malcev superalgebra on one odd generator is constructed. Some corollaries for central skew-symmetric elements in free Malcev and free alternative algebras are obtained. In particular, the Malcev Grassmann algebra is constructed.

Mathematics Subject Classification:

ACKNOWLEDGMENTS

Ivan Shestakov is partially supported by CNPq, grant 304633/03-8. Natalia Zhukavets is partially supported by the Institutional Grant MSM 6840770010, Czech Republic, and by FAPESP, grant 03/01237-2.

Notes

Communicated by B. Allison.

1Note that on the preliminary stage of the proof of this proposition, the use of the computer program “Malcev” (Buchnev et al., Citation1998) was very useful.

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