Email this article Commutative Nilpotent Subalgebras with Nilpotency Index n-1 in the Algebra of Matrices of Order n
- Authors: Markova O.V.1
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Affiliations:
- M. V. Lomonosov Moscow State University
- Issue: Vol 224, No 6 (2017)
- Pages: 956-970
- Section: Article
- URL: https://journal-vniispk.ru/1072-3374/article/view/239729
- DOI: https://doi.org/10.1007/s10958-017-3465-6
- ID: 239729
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Abstract
The paper establishes the existence of an element with nilpotency index n − 1 in an arbitrary nilpotent commutative subalgebra with nilpotency index n−1 in the algebra of upper niltriangular matrices Nn(????) over a field ???? with at least n elements for all n ≥ 5, and also, as a corollary, in the full matrix algebra Mn(????). The result implies an improvement with respect to the base field of known classification theorems due to D. A. Suprunenko, R. I. Tyshkevich, and I. A. Pavlov for algebras of the class considered.
About the authors
O. V. Markova
M. V. Lomonosov Moscow State University
Author for correspondence.
Email: ov_markova@mail.ru
Russian Federation, Moscow
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