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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.07108 |
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| _version_ | 1866912698598424576 |
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| author | Liu, Linlin Zheng, Huihui |
| author_facet | Liu, Linlin Zheng, Huihui |
| contents | Family algebraic structures indexed by a semigroup arise naturally in renormalizations of quantum field theory. In this paper, we first define the notion of $Ω$-associative $H$-pseudoalgebra, where the operations are indexed by pairs of elements from a semigroup $Ω$. Then we construct $Ω$-associative $H$-pseudoalgebras from associative $H$-pseudoalgebras, $Ω$-associative algebras, Rota-Baxter family algebras, $Ω$-type $H$-pseudoalgebras and family-type $H$-pseudoalgebras. Moreover, we investigate the cohomology of $Ω$-associative $H$-pseudoalgebras and establish that it both induces the cohomology of pseudo-$\mathcal{O}$-operator families and governs the associated formal deformations. As an application, we show that the first-order deformation of a commutative $Ω$-associative $H$-pseudoalgebra yields an $Ω$-Poisson $H$-pseudoalgebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07108 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Associative $H$-pseudoalgebras with a semigroup Liu, Linlin Zheng, Huihui Rings and Algebras Family algebraic structures indexed by a semigroup arise naturally in renormalizations of quantum field theory. In this paper, we first define the notion of $Ω$-associative $H$-pseudoalgebra, where the operations are indexed by pairs of elements from a semigroup $Ω$. Then we construct $Ω$-associative $H$-pseudoalgebras from associative $H$-pseudoalgebras, $Ω$-associative algebras, Rota-Baxter family algebras, $Ω$-type $H$-pseudoalgebras and family-type $H$-pseudoalgebras. Moreover, we investigate the cohomology of $Ω$-associative $H$-pseudoalgebras and establish that it both induces the cohomology of pseudo-$\mathcal{O}$-operator families and governs the associated formal deformations. As an application, we show that the first-order deformation of a commutative $Ω$-associative $H$-pseudoalgebra yields an $Ω$-Poisson $H$-pseudoalgebra. |
| title | Associative $H$-pseudoalgebras with a semigroup |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2511.07108 |