Hom-Novikov超代数与Hom-anti-pre-Novikov超代数的若干结果
Some results on Hom-Novikov superalgebras and Hom-anti-pre-Novikov superalgebras
AI总结：
本文研究Hom-Novikov超代数的结构等性质，引入Hom-anti-pre-Novikov超代数，建立相关等价性、算子刻画及泊松型结构联系，明确其与可逆反超-𝒪-算子的基本关系。
AI中文摘要：
本文研究Hom-Novikov超代数的结构性质、算子表示及代数对偶性，并引入Hom-anti-pre-Novikov超代数。我们通过q-超代数扩张建立Hom-Novikov超代数与可容许Hom-Novikov超代数间的形式等价性，证明Hom-预李超代数具有Hom-Novikov结构当且仅当其关联2-超代数是可容许的。在超交换Hom-结合超代数上引入q-可容许对(𝒫,𝒬)，详细阐述Hom-Novikov超代数的系统构造及其可容许类。此外，我们刻画Hom-李超代数上的反超-𝒪-算子，证明可逆算子诱导相容Hom-anti-pre-李结构并直接扩展至可容许设置。将这些框架推广到泊松型结构，我们证明Hom-anti-pre-李泊松超代数的次相邻Hom-李超代数可得到转置Hom-泊松超代数。最后，建立Hom-anti-pre-Novikov超代数与可逆反超-𝒪-算子间的基本联系。
英文摘要：
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.
