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arXiv · 1705.01039

Polynomial bound for the nilpotency index of finitely generated nil algebras

M. Domokos
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Abstract

Working over an infinite field of positive characteristic, an upper bound is given for the nilpotency index of a finitely generated nil algebra of bounded nil index $n$ in terms of the maximal degree in a minimal homogenous generating system of the ring of simultaneous conjugation invariants of tuples of $n$ by $n$ matrices. This is deduced from a result of Zubkov. As a consequence, a recent degree bound due to Derksen and Makam for the generators of the ring of matrix invariants yields an upper bound for the nilpotency index of a finitely generated nil algebra that is polynomial in the number of generators and the nil index. Furthermore, a characteristic free treatment is given to Kuzmin's lower bound for the nilpotency index.

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BibTeXRIS

M. Domokos. 2018-03-31. Polynomial bound for the nilpotency index of finitely generated nil algebras. https://doi.org/10.2140/ant.2018.12.1233

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