Degenerations of 3-dimensional nilpotent associative algebras over an algebraically closed field

N. M. Ivanova; C. A. Pallikaros

doi:10.3842/umzh.v76i11.7987

N. M. Ivanova Institute of Mathematics of NAS of Ukraine, Kyiv; Ukraine and European University of Cyprus, Nicosia, Cyprus
C. A. Pallikaros Department of Mathematics and Statistics, University of Cyprus, Nicosia, Cyprus

DOI: https://doi.org/10.3842/umzh.v76i11.7987

Keywords: degeneration; orbit closure; nilpotent associative algebra

Abstract

UDC 512.5+514

We determine the complete degeneration picture inside the variety of nilpotent associative algebras of dimension three over an algebraically closed field. As compared with the discussion in [N. M. Ivanova, C. A. Pallikaros, Adv. Group Theory and Appl., 18, 41-79 (2024)], for some arguments in the present article, it is necessary to develop alternative techniques, which are now valid over an arbitrary algebraically closed field. There is a dichotomy of cases concerning the obtained results corresponding to the cases where the characteristic of the field is $2$ or not.

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