Polynomial identities for tangent algebras of monoassociative loops
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2011
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| _version_ | 1866908456082997248 |
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| author | Bremner, Murray R. Madariaga, Sara |
| author_facet | Bremner, Murray R. Madariaga, Sara |
| contents | We introduce degree n Sabinin algebras, which are defined by the polynomial identities up to degree n in a Sabinin algebra. Degree 4 Sabinin algebras can be characterized by the polynomial identities satisfied by the commutator, associator and two quaternators in the free nonassociative algebra. We consider these operations in a free power associative algebra and show that one of the quaternators is redundant. The resulting algebras provide the natural structure on the tangent space at the identity element of an analytic loop for which all local loops satisfy monoassociativity, a^2 a = a a^2. These algebras are the next step beyond Lie, Malcev, and Bol algebras. We also present an identity of degree 5 which is satisfied by these three operations but which is not implied by the identities of lower degree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1111_6113 |
| institution | arXiv |
| publishDate | 2011 |
| record_format | arxiv |
| spellingShingle | Polynomial identities for tangent algebras of monoassociative loops Bremner, Murray R. Madariaga, Sara Rings and Algebras 17A42, 20N05 We introduce degree n Sabinin algebras, which are defined by the polynomial identities up to degree n in a Sabinin algebra. Degree 4 Sabinin algebras can be characterized by the polynomial identities satisfied by the commutator, associator and two quaternators in the free nonassociative algebra. We consider these operations in a free power associative algebra and show that one of the quaternators is redundant. The resulting algebras provide the natural structure on the tangent space at the identity element of an analytic loop for which all local loops satisfy monoassociativity, a^2 a = a a^2. These algebras are the next step beyond Lie, Malcev, and Bol algebras. We also present an identity of degree 5 which is satisfied by these three operations but which is not implied by the identities of lower degree. |
| title | Polynomial identities for tangent algebras of monoassociative loops |
| topic | Rings and Algebras 17A42, 20N05 |
| url | https://arxiv.org/abs/1111.6113 |