Salvato in:
| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2508.17529 |
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Sommario:
- Family algebraic structures indexed by a semigroup first appeared in the algebraic aspects of renormalizations in quantum field theory. In this paper, we first introduce the concept of Nijenhuis family $Ω$-associative algebras and we discuss the relationship between Nijenhuis family and other operators families on $Ω$-associative algebras. Then, we define the cohomology theory of Nijenhuis family $Ω$-associative algebras and show that this cohomology controls the corresponding deformations. Finally, we study abelian extensions of Nijenhuis family $Ω$-associative algebras in terms of the second cohomology group.