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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.15333 |
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| _version_ | 1866914687495438336 |
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| author | Sun, Qinxiu Li, Zhen |
| author_facet | Sun, Qinxiu Li, Zhen |
| contents | The goal of the present paper is to investigate non-abelian extensions of Lie-Yamaguti algebras and explore extensibility of a pair of automorphisms about a non-abelian extension of Lie-Yamaguti algebras. First, we study non-abelian extensions of Lie-Yamaguti algebras and classify the non-abelian extensions in terms of non-abelian cohomology groups. Next, we characterize the non-abelian extensions in terms of Maurer-Cartan elements. Moreover, we discuss the equivalent conditions of the extensibility of a pair of automorphisms about a non-abelian extension of Lie-Yamaguti algebras, and derive the fundamental sequences of Wells in the context of Lie-Yamaguti algebras. Finally, we discuss the previous results in the case of abelian extensions of Lie-Yamaguti algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15333 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-abelian extensions and Wells exact sequences of Lie-Yamaguti algebras Sun, Qinxiu Li, Zhen Rings and Algebras The goal of the present paper is to investigate non-abelian extensions of Lie-Yamaguti algebras and explore extensibility of a pair of automorphisms about a non-abelian extension of Lie-Yamaguti algebras. First, we study non-abelian extensions of Lie-Yamaguti algebras and classify the non-abelian extensions in terms of non-abelian cohomology groups. Next, we characterize the non-abelian extensions in terms of Maurer-Cartan elements. Moreover, we discuss the equivalent conditions of the extensibility of a pair of automorphisms about a non-abelian extension of Lie-Yamaguti algebras, and derive the fundamental sequences of Wells in the context of Lie-Yamaguti algebras. Finally, we discuss the previous results in the case of abelian extensions of Lie-Yamaguti algebras. |
| title | Non-abelian extensions and Wells exact sequences of Lie-Yamaguti algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2401.15333 |