Deformation Cohomology of Lie-Yamaguti algebras and Free Lie-Yamaguti algebras
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912406644457472 |
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| author | Goswami, Saikat |
| author_facet | Goswami, Saikat |
| contents | Infinitesimal deformation theory of Lie-Yamaguti algebras was introduced by Tao Zhang and Juan Li . We extend their theory to develop formal one-parameter deformation theory of Lie-Yamaguti algebras. It turns out that the right deformation cohomology which controls deformations in this context, is a variant of Lie-Yamaguti algebra cohomology which we introduce in this paper. At the end, we introduce the free object in the category of Lie-Yamaguti algebras and prove that it is rigid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_03655 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Deformation Cohomology of Lie-Yamaguti algebras and Free Lie-Yamaguti algebras Goswami, Saikat Rings and Algebras 17A30, 17A40, 17A42, 17D99 Infinitesimal deformation theory of Lie-Yamaguti algebras was introduced by Tao Zhang and Juan Li . We extend their theory to develop formal one-parameter deformation theory of Lie-Yamaguti algebras. It turns out that the right deformation cohomology which controls deformations in this context, is a variant of Lie-Yamaguti algebra cohomology which we introduce in this paper. At the end, we introduce the free object in the category of Lie-Yamaguti algebras and prove that it is rigid. |
| title | Deformation Cohomology of Lie-Yamaguti algebras and Free Lie-Yamaguti algebras |
| topic | Rings and Algebras 17A30, 17A40, 17A42, 17D99 |
| url | https://arxiv.org/abs/2308.03655 |