Varieties of initial dialgebras and some of their Koszul dual operads
Aigerim Dauletiyarova, Abdenacer Makhlouf, and Bauyrzhan Sartayev

TL;DR
This paper introduces a universal method for constructing initial dialgebra varieties from a given algebraic variety and provides bases for free initial Lie and associative dialgebras.
Contribution
It presents a universal algorithm for initial dialgebra varieties and constructs bases for free initial Lie and associative dialgebras.
Findings
Constructed a basis for free initial Lie dialgebras.
Constructed a basis for free initial associative dialgebras.
Provided a method to recover algebras from subvarieties of dialgebras.
Abstract
In this paper, for a given variety , we present a universal algorithm for constructing a subvariety of -dialgebras from which one can recover an algebra belonging to . Such a subvariety is called the variety of initial -dialgebras. In addition, we construct a basis of the free initial Lie and associative dialgebras.
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