Classification of Associative Algebras Satisfying Quadratic Polynomial Identities
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915657881223168 |
|---|---|
| author | Rocha, Josimar da Silva |
| author_facet | Rocha, Josimar da Silva |
| contents | In quantum mechanics, associative algebras play an important role in understanding symmetries and operator algebras, providing new algebraic frameworks for describing physical systems. This work classifies associative algebras over a field K that are generated by a finite set G and satisfy a polynomial identity of the form X^{2} = aX+b, where a and b are elements of K and X varies either over all elements of the algebra or over all elements of the multiplicative semigroup S generated by G. One of the results obtained in this work shows that algebras satisfying X^{2}=0 over fields of characteristics different from 2 are nilpotent of index 3.
The results were computationally validated using the GAP system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06125 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classification of Associative Algebras Satisfying Quadratic Polynomial Identities Rocha, Josimar da Silva Rings and Algebras 16R10 (primary), 16N40, 16R40 (secondary) G.2.1; F.1.3 In quantum mechanics, associative algebras play an important role in understanding symmetries and operator algebras, providing new algebraic frameworks for describing physical systems. This work classifies associative algebras over a field K that are generated by a finite set G and satisfy a polynomial identity of the form X^{2} = aX+b, where a and b are elements of K and X varies either over all elements of the algebra or over all elements of the multiplicative semigroup S generated by G. One of the results obtained in this work shows that algebras satisfying X^{2}=0 over fields of characteristics different from 2 are nilpotent of index 3. The results were computationally validated using the GAP system. |
| title | Classification of Associative Algebras Satisfying Quadratic Polynomial Identities |
| topic | Rings and Algebras 16R10 (primary), 16N40, 16R40 (secondary) G.2.1; F.1.3 |
| url | https://arxiv.org/abs/2512.06125 |