Derivations, Cohomology and Deformation of BiHom-Associative Dialgebra
Ahmed Zahari, Sania Asif

TL;DR
This paper introduces BiHom-associative dialgebras, classifies their derivations, extends cohomology theory to these structures, and explores their formal deformations, advancing the understanding of BiHom algebraic systems.
Contribution
It defines BiHom-associative dialgebras, classifies their derivations, and extends cohomology and deformation theory to these new algebraic structures.
Findings
Complete classification of derivations for 2- and 3-dimensional cases.
Extension of cohomology theory to BiHom-associative dialgebras.
Evaluation of formal deformations using cohomology.
Abstract
Due to the immense importance of BiHom Type algebras and cohomology of various algebraic structures, this paper is devoted to defining the BiHom-associative dialgebra, its derivation, generalized derivation, and quasi-derivation. We provided the complete classification of these derivations of and -dimensional BiHom-associative dialgebras. We further generalized the cohomology of BiHom-associative algebras to the cohomology of BiHom-associative dialgebras. As an application to cohomology, we evaluate the one-parameter formal deformation of BiHom-associative dialgebras.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology
