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arXiv · 2508.17529

Cohomology theory of Nijenhuis family $\Omega$-associative algebras

Sami Benabdelhafidh
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Abstract

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 $\Omega$-associative algebras and we discuss the relationship between Nijenhuis family and other operators families on $\Omega$-associative algebras. Then, we define the cohomology theory of Nijenhuis family $\Omega$-associative algebras and show that this cohomology controls the corresponding deformations. Finally, we study abelian extensions of Nijenhuis family $\Omega$-associative algebras in terms of the second cohomology group.

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Sami Benabdelhafidh. 2025-08-24. Cohomology theory of Nijenhuis family $\Omega$-associative algebras. https://arxiv.org/abs/2508.17529

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