Sweedler Duality for BiHom-associative Algebras
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912859229782016 |
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| author | Sun, Jiacheng |
| author_facet | Sun, Jiacheng |
| contents | Motivated by the fact that ordinary linear duality does not in general produce a coalgebra structure from an infinite-dimensional algebra, we develop a Sweedler-type finite dual construction for BiHom-associative algebras. For a BiHom-algebra $(G,μ,α,β)$ over a field, we define its Sweedler dual $G^{\circ}\subseteq G^{*}$ as the subspace of linear functionals annihilating a finite-codimensional BiHom-ideal of $G$. We prove that $G^{\circ}$ carries a natural BiHom-coalgebra structure whose comultiplication is the restriction of $μ^{*}$, and that BiHom-algebra morphisms induce BiHom-coalgebra morphisms on Sweedler duals. We further extend this construction to right BiHom-modules, obtaining right BiHom-comodules over $G^{\circ}$ under a surjectivity assumption on the twisting map $β$. The Hom and classical cases are recovered by the specializations $α=β$ and $α=β=\mathrm{Id}$, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21730 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sweedler Duality for BiHom-associative Algebras Sun, Jiacheng Rings and Algebras Primary 17A30, Secondary 17A60, 17D30 Motivated by the fact that ordinary linear duality does not in general produce a coalgebra structure from an infinite-dimensional algebra, we develop a Sweedler-type finite dual construction for BiHom-associative algebras. For a BiHom-algebra $(G,μ,α,β)$ over a field, we define its Sweedler dual $G^{\circ}\subseteq G^{*}$ as the subspace of linear functionals annihilating a finite-codimensional BiHom-ideal of $G$. We prove that $G^{\circ}$ carries a natural BiHom-coalgebra structure whose comultiplication is the restriction of $μ^{*}$, and that BiHom-algebra morphisms induce BiHom-coalgebra morphisms on Sweedler duals. We further extend this construction to right BiHom-modules, obtaining right BiHom-comodules over $G^{\circ}$ under a surjectivity assumption on the twisting map $β$. The Hom and classical cases are recovered by the specializations $α=β$ and $α=β=\mathrm{Id}$, respectively. |
| title | Sweedler Duality for BiHom-associative Algebras |
| topic | Rings and Algebras Primary 17A30, Secondary 17A60, 17D30 |
| url | https://arxiv.org/abs/2601.21730 |