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arXiv · 2608.15346

Some results on Hom-Novikov superalgebras and Hom-anti-pre-Novikov superalgebras

Wiem Ben Abdelhafidh
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Abstract

This paper investigates the structural properties, operator representations, and algebraic duality of Hom-Novikov superalgebras and to introduce Hom-anti-pre-Novikov superalgebras. We establish a formal equivalence between Hom-Novikov superalgebras and admissible Hom-Novikov superalgebras via $q$-superalgebra extensions, proving that a Hom-pre-Lie superalgebra admits a Hom-Novikov structure if and only if its associated $2$-superalgebra is admissible. Introducing $q$-admissible pairs $(\mathcal P, \mathcal Q)$ on super-commutative Hom-associative superalgebras, we detail systematic constructions of Hom-Novikov superalgebras and their admissibility classes. Furthermore, we characterize anti-super-$\mathcal{O}$-operators on Hom-Lie superalgebras, showing that invertible operators induce compatible Hom-anti-pre-Lie structures and extend directly to admissible setups. Extending these frameworks to Poisson-type structures, we demonstrate that the sub-adjacent Hom-Lie superalgebra of a Hom-anti-pre-Lie Poisson superalgebra yields a transposed Hom-Poisson superalgebra. Finally, we establish the fundamental connection between Hom-anti-pre-Novikov superalgebras and invertible anti-super-$\mathcal{O}$-operators.

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Wiem Ben Abdelhafidh. 2026-08-15. Some results on Hom-Novikov superalgebras and Hom-anti-pre-Novikov superalgebras. https://arxiv.org/abs/2608.15346

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