Subalgebras of free algebras

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

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

Subalgebras of free algebras
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by A. A. Mikhalev, V. E. Shpilrain and A. A. Zolotykh

Proc. Amer. Math. Soc. 124 (1996), 1977-1984

DOI: https://doi.org/10.1090/S0002-9939-96-03593-9

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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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