$\delta$-Leibniz algebras and related $\delta$-type algebras
Jobir Adashev, Ivan Kaygorodov

TL;DR
This paper explores $oldsymbol{ ext{delta}}$-Leibniz algebras, a parametric generalization of Leibniz algebras, defining related algebraic structures and analyzing their properties and connections to nilalgebras within a unified framework.
Contribution
It introduces $oldsymbol{ ext{delta}}$-Leibniz and related algebras, establishing their properties and relationships, thus broadening the understanding of non-associative algebra classes through a parametric approach.
Findings
Defined $oldsymbol{ ext{delta}}$-Lie, $oldsymbol{ ext{delta}}$-Lie dialgebras, and $oldsymbol{ ext{delta}}$-Zinbiel algebras.
Established connections between $oldsymbol{ ext{delta}}$-Leibniz algebras and nilalgebras.
Provided a unified framework for various non-associative algebras using the $oldsymbol{ ext{delta}}$ parameter.
Abstract
This paper introduces and investigates the structure of -Leibniz algebras, which serve as a parametric generalization of classical Leibniz algebras defined by a scalar . The authors define -Lie algebras, -Lie dialgebras, and -Zinbiel algebras via a standard procedure and study their fundamental properties. Furthermore, the research describes symmetric -Leibniz algebras and algebras of -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 parameter.
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Mathematical Theories and Applications · Advanced Differential Geometry Research
