Classification of four-dimensional anti-dendriform algebras whose associated associative algebra has the center of dimension one

TL;DR

This paper classifies four-dimensional anti-dendriform algebras linked to four-dimensional associative algebras with a one-dimensional center, expanding understanding of their structure and classification.

Contribution

It provides a complete classification of four-dimensional anti-dendriform algebras associated with specific associative algebras, a previously uncharted area.

Findings

All such four-dimensional anti-dendriform algebras are classified.

The associated associative algebras have a one-dimensional center.

The classification aids in understanding the structure of anti-dendriform algebras.

Abstract

This article is devoted to the classification of anti-dendriform algebras that are associated with associativity. They are characterized as algebras with two operations whose sum is associative. In the paper all four-dimensional complex anti-dendriform algebras associated to four-dimensional associative algebras with one-dimensional center are classified