Anti-associative algebras
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866916200179564544 |
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| author | Remm, Elisabeth |
| author_facet | Remm, Elisabeth |
| contents | An anti-associative algebra is a nonassociative algebra whose multiplication satisfies the identity a(bc)+(ab)c=0. Such algebras are nilpotent. We describe the free anti-associative algebras with a finite number of generators. Other types of nonassociative algebras, obtained either by the process of polarization, such as Jacobi-Jordan algebras, or obtained by deformation quantization, are associated with this class of algebras. Following Markl-Remms work, we describe the operads associated with these algebra classes and in particular the cohomology complexes in relation to deformations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_10812 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Anti-associative algebras Remm, Elisabeth Rings and Algebras 17D99 An anti-associative algebra is a nonassociative algebra whose multiplication satisfies the identity a(bc)+(ab)c=0. Such algebras are nilpotent. We describe the free anti-associative algebras with a finite number of generators. Other types of nonassociative algebras, obtained either by the process of polarization, such as Jacobi-Jordan algebras, or obtained by deformation quantization, are associated with this class of algebras. Following Markl-Remms work, we describe the operads associated with these algebra classes and in particular the cohomology complexes in relation to deformations. |
| title | Anti-associative algebras |
| topic | Rings and Algebras 17D99 |
| url | https://arxiv.org/abs/2202.10812 |