Classification of four-dimensional anti-dendriform algebras whose associated associative algebra has a one-dimensional annihilator

Jobir Adashev; Artem Lopatin; Zafar Normatov; Shokhsanam Solijonova

doi:10.13069/jacodesmath.v13i3.410

Authors

Jobir Adashev Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan https://orcid.org/0000-0002-4882-4098
Artem Lopatin State University of Campinas, Campinas, Brazil https://orcid.org/0000-0003-2495-6050
Zafar Normatov School of Mathematics, Jilin University, Changchun, China https://orcid.org/0000-0001-7818-0441
Shokhsanam Solijonova Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan https://orcid.org/0009-0003-3516-5382

DOI:

https://doi.org/10.13069/jacodesmath.v13i3.410

Keywords:

Associative algebra , Anti-dendriform algebra, Nilpotent algebras

Abstract

This paper is devoted to the classification of four-dimensional anti-dendriform algebras over the field of complex numbers. Such algebras are defined by the presence of two binary operations whose sum determines an associative multiplication. The algebra obtained with respect to this multiplication is called the associated associative algebra, which is necessarily nilpotent. In the present paper, we obtain a classification of all four-dimensional anti-dendriform algebras associated with four-dimensional associative algebras whose annihilator is one-dimensional.

Received: 12 September 2025 | Accepted: 01 April 2026

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