On Hom-Analogues of Heaps and Trusses
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914016986660864 |
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| author | Anowar, Tarik Saha, Ripan Thokdar, Sayan |
| author_facet | Anowar, Tarik Saha, Ripan Thokdar, Sayan |
| contents | This paper develops the foundations of Hom-heaps, Hom-trusses, and Hom-braces as natural Hom-type analogues of their classical counterparts. We establish the correspondence between Hom-heaps and Hom-groups, showing that the retract of a Hom-heap at a point yields a Hom-group precisely when the point is fixed under the twisting map. Three interrelated definitions of Hom-trusses are introduced and their structural properties are investigated, including the construction of modules over Hom-trusses. For Hom-braces, we propose three variants and demonstrate their close connections with Hom-trusses, proving in particular that certain Hom-trusses naturally give rise to Hom-braces and vice versa. Our results provide a systematic framework that extends heap and truss theory into the Hom-algebraic setting, opening new perspectives for applications in Yang--Baxter theory, non-associative geometry, and categorical algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01578 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Hom-Analogues of Heaps and Trusses Anowar, Tarik Saha, Ripan Thokdar, Sayan Rings and Algebras Group Theory This paper develops the foundations of Hom-heaps, Hom-trusses, and Hom-braces as natural Hom-type analogues of their classical counterparts. We establish the correspondence between Hom-heaps and Hom-groups, showing that the retract of a Hom-heap at a point yields a Hom-group precisely when the point is fixed under the twisting map. Three interrelated definitions of Hom-trusses are introduced and their structural properties are investigated, including the construction of modules over Hom-trusses. For Hom-braces, we propose three variants and demonstrate their close connections with Hom-trusses, proving in particular that certain Hom-trusses naturally give rise to Hom-braces and vice versa. Our results provide a systematic framework that extends heap and truss theory into the Hom-algebraic setting, opening new perspectives for applications in Yang--Baxter theory, non-associative geometry, and categorical algebra. |
| title | On Hom-Analogues of Heaps and Trusses |
| topic | Rings and Algebras Group Theory |
| url | https://arxiv.org/abs/2509.01578 |