Novikov algebras in low dimension: identities, images and codimensions
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916608013762560 |
|---|---|
| author | Santos, Iritan Ferreira dos Kuz'min, Alexey M. Lopatin, Artem |
| author_facet | Santos, Iritan Ferreira dos Kuz'min, Alexey M. Lopatin, Artem |
| contents | Polynomial identities of two-dimensional Novikov algebras are studied over the complex field $\mathbb{C}$. We determine minimal generating sets for the T-ideals of the polynomial identities and linear bases for the corresponding relatively free algebras. As a consequence, we establish that polynomial identities separate two-dimensional Novikov algebras, which are not associative. Namely, any two-dimensional Novikov algebras, which are not associative, are isomorphic if and only if they satisfy the same polynomial identities. Moreover, we obtain the codimension sequences of all these algebras. In particular, every two-dimensional Novikov algebra has at most linear growth of its codimension sequence. We explicitly describe multilinear images of every two-dimensional Novikov algebra. In particular, we show that these images are vector spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03184 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Novikov algebras in low dimension: identities, images and codimensions Santos, Iritan Ferreira dos Kuz'min, Alexey M. Lopatin, Artem Rings and Algebras 17A30, 17A50, 17D25, 17D99 Polynomial identities of two-dimensional Novikov algebras are studied over the complex field $\mathbb{C}$. We determine minimal generating sets for the T-ideals of the polynomial identities and linear bases for the corresponding relatively free algebras. As a consequence, we establish that polynomial identities separate two-dimensional Novikov algebras, which are not associative. Namely, any two-dimensional Novikov algebras, which are not associative, are isomorphic if and only if they satisfy the same polynomial identities. Moreover, we obtain the codimension sequences of all these algebras. In particular, every two-dimensional Novikov algebra has at most linear growth of its codimension sequence. We explicitly describe multilinear images of every two-dimensional Novikov algebra. In particular, we show that these images are vector spaces. |
| title | Novikov algebras in low dimension: identities, images and codimensions |
| topic | Rings and Algebras 17A30, 17A50, 17D25, 17D99 |
| url | https://arxiv.org/abs/2502.03184 |