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<p>We determine the complete picture of degeneration inside the variety of nilpotent associative algebras of dimension three over an algebraically closed field. As compared with the discussion in [N. M. Ivanova and C. A. Pallikaros, <i>Adv. Group Theory Appl.</i>, <b>18</b>, 41–79 (2024)], for some arguments in the present paper, it is necessary to develop alternative techniques valid over an arbitrary algebraically closed field. There exists a dichotomy of cases concerning the accumulated results corresponding to the cases where the characteristic of the field is equal to 2 or not.</p>

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Degenerations of 3-Dimensional Nilpotent Associative Algebras over an Algebraically Closed Field

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • N. M. Ivanova,
  • C. A. Pallikaros

摘要

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