$\delta$-Leibniz algebras and related $\delta$-type algebras

Abstract

This paper introduces and investigates the structure of $\delta$-Leibniz algebras, which serve as a parametric generalization of classical Leibniz algebras defined by a scalar $\delta$. The authors define $\delta$-Lie algebras, $\delta$-Lie dialgebras, and $\delta$-Zinbiel algebras via a standard procedure and study their fundamental properties. Furthermore, the research describes symmetric $\delta$-Leibniz algebras and algebras of $\delta$-biderivation type, establishing their connections with nilalgebras. Finally, these results provide a unified framework for understanding various classes of non-associative algebras through the lens of the $\delta$ parameter.