On Affine Version of Hom-Lie Algebras
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914138561708032 |
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| author | Anowar, Tarik Saha, Ripan |
| author_facet | Anowar, Tarik Saha, Ripan |
| contents | This paper introduces Hom-type analogues of affine algebraic structures, termed Hom-affgebras. Extending Brzeziński's theory of affgebras and the Hom-algebra framework developed by Hartwig-Larsson-Silvestrov, we define and study Hom-associative, Hom-pre-Lie, and Hom-Lie affgebras, where the classical identities are twisted by an affine self-map. We show how Hom-associative, Hom-pre-Lie, and Hom-Lie affgebras are related to one another. The main focus of this paper is on Hom-Lie affgebras and their fibers. We study the concept of generalized derivations for Hom-Lie algebras, extending the notion of generalized derivations for Lie algebras. We explore the close relationship between Hom-Lie affgebras and such derivations. We show that every Hom-Lie affgebra both determines and is determined by a Hom-Lie algebra together with such a generalized derivation and a constant. Furthermore, we establish that a homomorphism between Lie affgebras corresponds to a homomorphism between their associated Lie fibers along with a constant, and vice versa. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17983 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Affine Version of Hom-Lie Algebras Anowar, Tarik Saha, Ripan Rings and Algebras This paper introduces Hom-type analogues of affine algebraic structures, termed Hom-affgebras. Extending Brzeziński's theory of affgebras and the Hom-algebra framework developed by Hartwig-Larsson-Silvestrov, we define and study Hom-associative, Hom-pre-Lie, and Hom-Lie affgebras, where the classical identities are twisted by an affine self-map. We show how Hom-associative, Hom-pre-Lie, and Hom-Lie affgebras are related to one another. The main focus of this paper is on Hom-Lie affgebras and their fibers. We study the concept of generalized derivations for Hom-Lie algebras, extending the notion of generalized derivations for Lie algebras. We explore the close relationship between Hom-Lie affgebras and such derivations. We show that every Hom-Lie affgebra both determines and is determined by a Hom-Lie algebra together with such a generalized derivation and a constant. Furthermore, we establish that a homomorphism between Lie affgebras corresponds to a homomorphism between their associated Lie fibers along with a constant, and vice versa. |
| title | On Affine Version of Hom-Lie Algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2510.17983 |