Subalgebras of free algebras

Mikhalev, A.; Shpilrain, V.; Zolotykh, A.

doi:10.1090/S0002-9939-96-03593-9

Subalgebras of free algebras

Authors: A. A. Mikhalev, V. E. Shpilrain and A. A. Zolotykh
Journal: Proc. Amer. Math. Soc. 124 (1996), 1977-1984
MSC (1991): Primary 17B01; Secondary 16S10, 13F20
DOI: https://doi.org/10.1090/S0002-9939-96-03593-9
MathSciNet review: 1350957
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Abstract: We use non-commutative Jacobian matrix to get information on finitely generated subalgebras of a free Lie algebra. In particular, we show that the rank of such a subalgebra is equal to the left rank (i.e., to the maximal number of left independent rows) of the corresponding Jacobian matrix; this also yields an effective procedure for finding the rank of a finitely generated subalgebra.

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Additional Information

A. A. Mikhalev
Affiliation: Department of Mechanics and Mathematics, Moscow State University, Moscow 119899, Russia
Email: aamikh@cnit.math.msu.su

V. E. Shpilrain
Affiliation: Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany
Address at time of publication: Department of Mathematics, University of California, Santa Barbara, California 93106
Email: shpil@math.ucsb.edu

A. A. Zolotykh
Affiliation: Department of Mechanics and Mathematics, Moscow State University, Moscow 119899, Russia
Email: zolotykh@cnit.math.msu.su

DOI: https://doi.org/10.1090/S0002-9939-96-03593-9
Received by editor(s): January 9, 1995
Additional Notes: The first and third authors were partially supported by the Russian Foundation for Fundamental Research, by the International Science Foundation, and by INTAS
The second author was supported by MINERVA Fellowship.
Communicated by: Lance W. Small
Article copyright: © Copyright 1996 American Mathematical Society