What does this research mean for the field?

BiHom-superdialgebras and BiHom-Leibniz superalgebras can be formally defined as generalizations of Hom-superdialgebras and BiHom-dialgebras, exhibiting stable properties under Rota-Baxter, Nijenhuis, and averaging operators. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To introduce BiHom-superdialgebras and BiHom-Leibniz superalgebras and establish their algebraic properties, operator actions, and structural connections.

August 29, 2026AxiomsOpen Access

BiHom-Superdialgebras and Associated BiHom-Leibniz Superalgebras

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Authors

NMNil MansuroğluAhi Evran University BMBouzid MosbahiUniversity of Sfax

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Implication

Theoretical study demonstrates operator actions and structural extensions in BiHom-superdialgebras, highlighting systematic constructions of BiHom-Leibniz superalgebras.

Key Points

To introduce BiHom-superdialgebras and BiHom-Leibniz superalgebras and establish their algebraic properties, operator actions, and structural connections.
Extended Hom-superdialgebras and BiHom-dialgebras to superalgebra settings involving two commuting homomorphisms.
Characterized operator-induced structural deformations using Rota–Baxter, Nijenhuis, and averaging operators.
Formulated the theory of actions, semidirect products, and functorial relationships in the purely even setting.
Proved that actions of Rota–Baxter, Nijenhuis, and averaging operators generate valid new BiHom-superdialgebra structures.
Constructed BiHom-Leibniz superalgebras from regular BiHom-superdialgebras possessing coinciding products and established BiHom-Poisson superdialgebras as a generalized framework.
Demonstrated the compatibility of the Leibniz functor with semidirect products in the purely even case.

Cite This Study

Mansuroğlu et al. (2026) studied this question.

synapsesocial.com/papers/6a9299958e5d7d1fc0c119fe https://doi.org/10.3390/axioms15090635

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Implication

Theoretical study demonstrates operator actions and structural extensions in BiHom-superdialgebras, highlighting systematic constructions of BiHom-Leibniz superalgebras.

BiHom-Superdialgebras and Associated BiHom-Leibniz Superalgebras

Discussion

Member takes

Implication

Key Points

Cite This Study

BiHom-Superdialgebras and Associated BiHom-Leibniz Superalgebras

Discussion

Member takes

Implication

Key Points

Cite This Study

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