Gröbner bases and dimension formulas for ternary partially associative operads
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2018
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911307217764352 |
|---|---|
| author | Bagherzadeh, Fatemeh Bremner, Murray |
| author_facet | Bagherzadeh, Fatemeh Bremner, Murray |
| contents | Dotsenko and Vallette discovered an extension to nonsymmetric operads of Buchberger's algorithm for Gröbner bases of polynomial ideals. In the free nonsymmetric operad with one ternary operation $({\ast}{\ast}{\ast})$, we compute a Gröbner basis for the ideal generated by partial associativity $((abc)de) + (a(bcd)e) + (ab(cde)$. In the category of $\mathbb{Z}$-graded vector spaces with Koszul signs, the (homological) degree of $({\ast}{\ast}{\ast})$ may be even or odd. We use the Gröbner bases to calculate the dimension formulas for these operads. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1810_04042 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Gröbner bases and dimension formulas for ternary partially associative operads Bagherzadeh, Fatemeh Bremner, Murray Rings and Algebras Combinatorics Primary 18D50. Secondary 17A30, 17A40, 17A50 Dotsenko and Vallette discovered an extension to nonsymmetric operads of Buchberger's algorithm for Gröbner bases of polynomial ideals. In the free nonsymmetric operad with one ternary operation $({\ast}{\ast}{\ast})$, we compute a Gröbner basis for the ideal generated by partial associativity $((abc)de) + (a(bcd)e) + (ab(cde)$. In the category of $\mathbb{Z}$-graded vector spaces with Koszul signs, the (homological) degree of $({\ast}{\ast}{\ast})$ may be even or odd. We use the Gröbner bases to calculate the dimension formulas for these operads. |
| title | Gröbner bases and dimension formulas for ternary partially associative operads |
| topic | Rings and Algebras Combinatorics Primary 18D50. Secondary 17A30, 17A40, 17A50 |
| url | https://arxiv.org/abs/1810.04042 |